Cremona's table of elliptic curves

975 = 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	975h	Isogeny class
Conductor	975	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-494325 = -1 · 32 · 52 · 133	Discriminant
Eigenvalues	1 3- 5+ -3 -1 13- -5 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-46,-127]	[a1,a2,a3,a4,a6]
Generators	[13:32:1]	Generators of the group modulo torsion
j	-417267265/19773	j-invariant
L	3.1593865371669	L(r)(E,1)/r!
Ω	0.91646876722812	Real period
R	0.57455795733635	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15600bl1 62400q1 2925j1 975e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975h1

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	-	+	-3	-1	-	-5	-8	0	1	3	-8	-2	8	-11	-11	5	1	3	16	-4	12	-3	0	-2

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Quadratic twists for elliptic curve 975h1

-4	8	-3	5	-7	-11	13
15600bl1	62400q1	2925j1	975e1	47775k1	117975bl1	12675z1

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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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