Cremona's table of elliptic curves

1975 = 5² · 79

Field	Data	Notes
Atkin-Lehner	5+ 79+	Signs for the Atkin-Lehner involutions
Class	1975d	Isogeny class
Conductor	1975	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-240395031171875 = -1 · 57 · 795	Discriminant
Eigenvalues	2  1 5+ -3 -3 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,7492,-700481]	[a1,a2,a3,a4,a6]
Generators	[1834:28971:8]	Generators of the group modulo torsion
j	2976041775104/15385281995	j-invariant
L	5.6488246414037	L(r)(E,1)/r!
Ω	0.27950646799569	Real period
R	5.0524990368836	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	31600q2 126400j2 17775y2 395c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1975d2

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	1	+	-3	-3	-4	2	0	-4	0	7	-3	12	-4	12	-9	0	12	2	-8	-14	+	-4	-10	-8

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Quadratic twists for elliptic curve 1975d2

-4	8	-3	5	-7
31600q2	126400j2	17775y2	395c2	96775g2

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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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