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	7568g	Isogeny class
Conductor	7568	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	915728 = 24 · 113 · 43	Discriminant
Eigenvalues	2+ -2  2  1 11- -6 -6  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,43]	[a1,a2,a3,a4,a6]
Generators	[-3:11:1]	Generators of the group modulo torsion
j	233644288/57233	j-invariant
L	3.2853879640201	L(r)(E,1)/r!
Ω	2.6253680520623	Real period
R	0.41713363597906	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	3784b1 30272x1 68112i1 83248o1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7568g1

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	2	1	-	-6	-6	7	-5	7	5	2	6	-	3	-5	5	-5	-5	-12	-10	14	0	14	5

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Quadratic twists for elliptic curve 7568g1

-4	8	-3	-11
3784b1	30272x1	68112i1	83248o1

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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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