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	7568l	Isogeny class
Conductor	7568	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5157380096 = 213 · 114 · 43	Discriminant
Eigenvalues	2-  0  2  0 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7379,-243950]	[a1,a2,a3,a4,a6]
Generators	[225:3080:1]	Generators of the group modulo torsion
j	10848165325353/1259126	j-invariant
L	4.6510475860985	L(r)(E,1)/r!
Ω	0.51511382005383	Real period
R	2.257291206831	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	946a3 30272bb4 68112bn4 83248bj4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7568l3

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	2	0	-	2	2	-4	-8	2	0	2	10	+	0	-10	-4	2	-12	-8	6	4	-12	-6	-14

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Quadratic twists for elliptic curve 7568l3

-4	8	-3	-11
946a3	30272bb4	68112bn4	83248bj4

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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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