Cremona's table of elliptic curves

75712 = 2⁶ · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	75712s	Isogeny class
Conductor	75712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	875520	Modular degree for the optimal curve
Δ	-162590281957376 = -1 · 237 · 7 · 132	Discriminant
Eigenvalues	2+ -3 -3 7+  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-200044,-34443344]	[a1,a2,a3,a4,a6]
Generators	[190666:1753088:343]	Generators of the group modulo torsion
j	-19983597574473/3670016	j-invariant
L	2.3576684553754	L(r)(E,1)/r!
Ω	0.11287126477857	Real period
R	5.2220298517678	Regulator
r	1	Rank of the group of rational points
S	0.99999999959856	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712de1 2366m1 75712bl1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712s1

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
+	-3	-3	+	4	+	2	-4	-1	2	-10	4	-12	0	10	4	9	-13	2	15	2	4	-8	-14	-2

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Quadratic twists for elliptic curve 75712s1

-4	8	13
75712de1	2366m1	75712bl1

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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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