Cremona's table of elliptic curves

2975 = 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	5+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	2975c	Isogeny class
Conductor	2975	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	41184	Modular degree for the optimal curve
Δ	-4448699951171875 = -1 · 517 · 73 · 17	Discriminant
Eigenvalues	2 -2 5+ 7-  2  1 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-249908,48109719]	[a1,a2,a3,a4,a6]
j	-110470393399988224/284716796875	j-invariant
L	2.6239775262045	L(r)(E,1)/r!
Ω	0.43732958770075	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47600q1 26775br1 595a1 20825u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2975c1

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
2	-2	+	-	2	1	+	6	-9	6	5	7	-5	8	-9	-2	14	13	-2	-8	8	16	-1	-6	16

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Quadratic twists for elliptic curve 2975c1

-4	-3	5	-7	17
47600q1	26775br1	595a1	20825u1	50575e1

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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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