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	75712ct	Isogeny class
Conductor	75712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-6551207936 = -1 · 215 · 7 · 134	Discriminant
Eigenvalues	2- -1  1 7- -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-225,-4031]	[a1,a2,a3,a4,a6]
Generators	[21:8:1]	Generators of the group modulo torsion
j	-1352/7	j-invariant
L	4.2640043012881	L(r)(E,1)/r!
Ω	0.55526788693507	Real period
R	1.919796011625	Regulator
r	1	Rank of the group of rational points
S	1.0000000005634	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712bx1 37856f1 75712ca1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712ct1

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	1	-	-4	+	-6	-4	-1	6	6	-4	8	-4	6	-4	-3	-7	14	9	2	-12	16	2	-2

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Quadratic twists for elliptic curve 75712ct1

-4	8	13
75712bx1	37856f1	75712ca1

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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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