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	75712f	Isogeny class
Conductor	75712	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-230288061366272 = -1 · 219 · 7 · 137	Discriminant
Eigenvalues	2+ -1  0 7+ -3 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-169411233,-848657634527]	[a1,a2,a3,a4,a6]
Generators	[2286099717769:-69080762779040:148035889]	Generators of the group modulo torsion
j	-424962187484640625/182	j-invariant
L	3.4031020062124	L(r)(E,1)/r!
Ω	0.020923484324778	Real period
R	20.330636340181	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712cn3 2366a3 5824i3	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712f3

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	+	-3	+	0	2	-3	0	-5	-7	-3	-8	3	12	6	1	5	-12	-11	-1	12	18	-17

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Quadratic twists for elliptic curve 75712f3

-4	8	13
75712cn3	2366a3	5824i3

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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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