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	7568m	Isogeny class
Conductor	7568	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	7568 = 24 · 11 · 43	Discriminant
Eigenvalues	2-  2  0  1 11-  2  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-198,-1009]	[a1,a2,a3,a4,a6]
Generators	[-10373:117:1331]	Generators of the group modulo torsion
j	53925088000/473	j-invariant
L	6.0280528492474	L(r)(E,1)/r!
Ω	1.2721867132748	Real period
R	4.7383397313827	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	1892c1 30272bc1 68112bk1 83248bm1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7568m1

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	0	1	-	2	0	-5	-3	-3	-5	-10	-6	+	-3	3	-9	-7	13	0	2	4	-6	6	5

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Quadratic twists for elliptic curve 7568m1

-4	8	-3	-11
1892c1	30272bc1	68112bk1	83248bm1

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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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