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	975a	Isogeny class
Conductor	975	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2867803316015625 = -1 · 32 · 58 · 138	Discriminant
Eigenvalues	1 3+ 5+  0  4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,15125,-2468750]	[a1,a2,a3,a4,a6]
Generators	[250:4000:1]	Generators of the group modulo torsion
j	24487529386319/183539412225	j-invariant
L	2.6002925141077	L(r)(E,1)/r!
Ω	0.22488407003775	Real period
R	2.8907033229067	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15600bz6 62400cs5 2925g6 195a6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975a6

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	+	+	0	4	+	-2	-4	-8	-2	-8	-6	-6	4	8	-6	-12	-2	4	0	6	16	4	10	-18

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Quadratic twists for elliptic curve 975a6

-4	8	-3	5	-7	-11	13
15600bz6	62400cs5	2925g6	195a6	47775cp5	117975p5	12675e6

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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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