Cremona's table of elliptic curves

7568 = 2⁴ · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 11- 43-	Signs for the Atkin-Lehner involutions
Class	7568n	Isogeny class
Conductor	7568	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	8160	Modular degree for the optimal curve
Δ	-10080333824 = -1 · 212 · 113 · 432	Discriminant
Eigenvalues	2- -1 -1  0 11- -2  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16101,-781043]	[a1,a2,a3,a4,a6]
j	-112706583998464/2461019	j-invariant
L	1.2714660845773	L(r)(E,1)/r!
Ω	0.21191101409622	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	473a1 30272v1 68112bs1 83248ba1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7568n1

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	0	-	-2	6	8	1	6	1	-3	-4	-	8	-14	-9	-4	-9	13	-16	-16	6	-7	13

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Quadratic twists for elliptic curve 7568n1

-4	8	-3	-11
473a1	30272v1	68112bs1	83248ba1

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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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