Cremona's table of elliptic curves

31768 = 2³ · 11 · 19²

Field	Data	Notes
Atkin-Lehner	2- 11- 19-	Signs for the Atkin-Lehner involutions
Class	31768j	Isogeny class
Conductor	31768	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	15552	Modular degree for the optimal curve
Δ	10232536336 = 24 · 116 · 192	Discriminant
Eigenvalues	2- -1 -1  0 11- -5  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-956,10609]	[a1,a2,a3,a4,a6]
Generators	[-28:121:1] [5:77:1]	Generators of the group modulo torsion
j	16746513664/1771561	j-invariant
L	6.7760897255411	L(r)(E,1)/r!
Ω	1.2477039417337	Real period
R	0.45257061784264	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63536c1 31768b1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 31768j1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-1	-1	0	-	-5	5	-	-9	-5	-8	-2	3	-1	-9	5	-5	1	9	-9	-3	-11	4	-15	-7

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Quadratic twists for elliptic curve 31768j1

-4	-19
63536c1	31768b1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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