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	75712m	Isogeny class
Conductor	75712	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3594240	Modular degree for the optimal curve
Δ	-7083200191503794176 = -1 · 220 · 72 · 1310	Discriminant
Eigenvalues	2+  2 -3 7+ -6 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7349697,7672758209]	[a1,a2,a3,a4,a6]
Generators	[1553:1344:1]	Generators of the group modulo torsion
j	-1214950633/196	j-invariant
L	4.687760713487	L(r)(E,1)/r!
Ω	0.22823600857063	Real period
R	2.5673866836992	Regulator
r	1	Rank of the group of rational points
S	1.00000000007	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712dc1 2366k1 75712bi1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712m1

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	-3	+	-6	+	-3	-4	-6	-3	10	-1	3	10	0	9	-6	7	2	0	7	14	-18	6	-2

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Quadratic twists for elliptic curve 75712m1

-4	8	13
75712dc1	2366k1	75712bi1

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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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