Cremona's table of elliptic curves

7636 = 2² · 23 · 83

Field	Data	Notes
Atkin-Lehner	2- 23+ 83+	Signs for the Atkin-Lehner involutions
Class	7636b	Isogeny class
Conductor	7636	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13920	Modular degree for the optimal curve
Δ	-33340040002352 = -1 · 24 · 232 · 835	Discriminant
Eigenvalues	2-  1  0 -3 -5  4 -1  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12453,598592]	[a1,a2,a3,a4,a6]
j	-13349363777536000/2083752500147	j-invariant
L	1.2652893573564	L(r)(E,1)/r!
Ω	0.63264467867822	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	30544t1 122176k1 68724g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7636b1

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	0	-3	-5	4	-1	2	+	-3	-5	3	-2	8	4	6	3	-1	8	10	8	0	+	-10	10

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Quadratic twists for elliptic curve 7636b1

-4	8	-3
30544t1	122176k1	68724g1

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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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