Cremona's table of elliptic curves

7644 = 2² · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	7644i	Isogeny class
Conductor	7644	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-1736227584 = -1 · 28 · 32 · 73 · 133	Discriminant
Eigenvalues	2- 3- -1 7-  2 13- -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,299,-169]	[a1,a2,a3,a4,a6]
Generators	[65:546:1]	Generators of the group modulo torsion
j	33554432/19773	j-invariant
L	4.8093166048499	L(r)(E,1)/r!
Ω	0.8750644034572	Real period
R	0.1526654808317	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	30576bz1 122304o1 22932u1 7644b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7644i1

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
-	-	-1	-	2	-	-6	-1	3	-7	7	-12	6	1	11	-7	-4	-2	-8	8	-5	1	-9	-11	-17

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Quadratic twists for elliptic curve 7644i1

-4	8	-3	-7	13
30576bz1	122304o1	22932u1	7644b1	99372bi1

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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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