Cremona's table of elliptic curves

1568 = 2⁵ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	1568h	Isogeny class
Conductor	1568	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	-2582630848 = -1 · 26 · 79	Discriminant
Eigenvalues	2-  2 -2 7- -4 -6  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-114,2528]	[a1,a2,a3,a4,a6]
Generators	[2:48:1]	Generators of the group modulo torsion
j	-64	j-invariant
L	3.300681707394	L(r)(E,1)/r!
Ω	1.2192864047003	Real period
R	2.7070602072408	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	1568f1 3136l1 14112w1 39200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1568h1

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	-	-4	-6	4	6	4	-6	-4	-6	-4	-12	-12	6	6	6	-12	-8	0	0	6	16	12

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Quadratic twists for elliptic curve 1568h1

-4	8	-3	5	-7
1568f1	3136l1	14112w1	39200q1	1568i1

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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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