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	75712g	Isogeny class
Conductor	75712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-620232704 = -1 · 219 · 7 · 132	Discriminant
Eigenvalues	2+ -1  3 7+  0 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,191,-703]	[a1,a2,a3,a4,a6]
Generators	[49:352:1]	Generators of the group modulo torsion
j	17303/14	j-invariant
L	6.3944635134062	L(r)(E,1)/r!
Ω	0.90127729088992	Real period
R	1.7737225759611	Regulator
r	1	Rank of the group of rational points
S	1.0000000001871	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712cp1 2366i1 75712bd1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712g1

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	3	+	0	+	6	-4	3	-6	10	8	0	-8	-6	-12	3	-11	2	3	-2	-4	0	6	-2

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Quadratic twists for elliptic curve 75712g1

-4	8	13
75712cp1	2366i1	75712bd1

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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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