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	7568b	Isogeny class
Conductor	7568	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	7568 = 24 · 11 · 43	Discriminant
Eigenvalues	2+  0  4  3 11+ -2  6  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-383,2885]	[a1,a2,a3,a4,a6]
j	388329202944/473	j-invariant
L	3.5255334161983	L(r)(E,1)/r!
Ω	3.5255334161983	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	3784e1 30272be1 68112z1 83248k1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7568b1

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
+	0	4	3	+	-2	6	5	3	1	-3	8	8	-	-9	-1	-7	1	-9	-12	-6	-2	-4	-8	17

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Quadratic twists for elliptic curve 7568b1

-4	8	-3	-11
3784e1	30272be1	68112z1	83248k1

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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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