Curve [0,0,0,0,-1516563] :	Using (a,b,c) search with (a,h) sieve and algebraic method
(with bigints to solve the syzygy)
Basic pair: I=0, J=40947201
disc=-1676673269734401
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
(a,h) sieving using 15 moduli: 
p:	9	5	7	11	17	23	29	41	43	47	53	59	71	83	89	
k_p:		1	2	1	1	1	1	1	2	1	1	1	1	1	1	
phi1:		4	3	7	8	7	23	9	19	26	36	50	53	79	2	
phi2:		*	5	*	*	*	*	*	28	*	*	*	*	*	*	
phi3:		*	6	*	*	*	*	*	39	*	*	*	*	*	*	
finished aux_init()
Before sorting, phi = (172.33682111256,298.49613018186),(172.33682111256,-298.49613018186),(-344.67364222512,0)
starting flag_init()
finished flag_init()
Looking for quartics with I = 0, J = 40947201
Looking for Type 3 quartics:
After  sorting, phi = (172.33682111256,298.49613018186),(172.33682111256,-298.49613018186),(-344.67364222512,0)
Basic a bound = 99.49871006062
Search range for a: (-99,66)
Search range for a: (-99,66)
Trying positive a from 1 up to 66 (square a first...)
Trying positive a from 1 up to 66 (...then non-square a)
Trying negative a from -1 down to -99
(-3,0,0,711,0)	(ipivot = -1, type = A) 	(0:00:0:0:0:0:0:00:0:0:0:0:0:0)	--trivial
(-27,0,0,237,0)	(ipivot = -1, type = A) 	(0:00:0:0:0:0:0:00:0:0:0:0:0:0)	--trivial
Finished looking for Type 3 quartics.
Looking for quartics with I = 0, J = 2620620864
Looking for Type 3 quartics:
After  sorting, phi = (689.34728445024,1193.9845207274),(689.34728445024,-1193.9845207274),(-1378.6945689005,0)
Basic a bound = 397.99484024248
Search range for a: (-397,265)
Search range for a: (-397,265)
Trying positive a from 1 up to 265 (square a first...)
(9,8,-4266,48600,-157707)	(ipivot = 1, type = B) 	(1:11:0:0:1:0:1:01:0:1:0:0:0:0)	--nontrivial...(x:y:z) = (1 : 3 : 0)
Point = [19209:511280:27]
	height = 8.86333898159
Doubling global 2-adic index to 2
global 2-adic index is equal to local index
so we abort the search for large quartics
Rank of B=im(eps) increases to 1 (pivotal prime =5)
Exiting search for large quartics after finding enough globally soluble ones.
1324974	 (a,b,c) triples in search region
221914	 failed c-divisiblity,
1102813	 failed syzygy sieve,
247	 passed sieve.
236	 failed syzygy after sieving,
6	 failed d-integrality,
7	 failed e-integrality,
0	 failed extra-2 divisibility conditions,
3	 passed all and produced quartics.
After getquartics(): 
n1 = 1
n2 = 1
n3 = 0
B-rank = 1
Mordell rank contribution from B=im(eps) = 1
Selmer  rank contribution from B=im(eps) = 1
Sha     rank contribution from B=im(eps) = 0
Mordell rank contribution from A=ker(eps) = 0
Selmer  rank contribution from A=ker(eps) = 0
Sha     rank contribution from A=ker(eps) = 0

Used full 2-descent via multiplication-by-2 map
Rank = 1
Rank of S^2(E)  = 1

Searching for points (bound = 8)...done:
  found points which generate a subgroup of rank 0
  and regulator 1
Processing points found during 2-descent...done:
2-descent increases rank to 1,   now regulator = 8.86333898159
Saturating (with bound = -1)...done:
  points were already saturated.
Transferring points from minimal curve [0,0,0,0,-1516563] back to original curve [0,0,0,0,-1516563]

Generator 1 is [19209:511280:27]; height 8.86333898159

Regulator = 8.86333898159

The rank and full Mordell-Weil basis have been determined unconditionally.

