Cremona's table of elliptic curves

1975 = 5² · 79

Field	Data	Notes
Atkin-Lehner	5+ 79+	Signs for the Atkin-Lehner involutions
Class	1975a	Isogeny class
Conductor	1975	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	6171875 = 57 · 79	Discriminant
Eigenvalues	1  0 5+  4  4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-52667,4665366]	[a1,a2,a3,a4,a6]
Generators	[11152994:176402478:29791]	Generators of the group modulo torsion
j	1034008400994561/395	j-invariant
L	3.7657887801095	L(r)(E,1)/r!
Ω	1.4341660737888	Real period
R	10.503075895976	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31600l4 126400b4 17775w3 395a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1975a4

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	4	-6	-6	-4	0	6	0	-10	2	-8	-12	14	-4	-10	4	-8	-2	+	-4	-6	-10

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Quadratic twists for elliptic curve 1975a4

-4	8	-3	5	-7
31600l4	126400b4	17775w3	395a4	96775d4

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

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