Cremona's table of elliptic curves

637 = 7² · 13

Field	Data	Notes
Atkin-Lehner	7- 13-	Signs for the Atkin-Lehner involutions
Class	637c	Isogeny class
Conductor	637	Conductor
∏ cp	7	Product of Tamagawa factors cp
Δ	-17724902963955733 = -1 · 710 · 137	Discriminant
Eigenvalues	1  0  0 7- -3 13- -7  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,30763,6051758]	[a1,a2,a3,a4,a6]
Generators	[-38:2216:1]	Generators of the group modulo torsion
j	11397810375/62748517	j-invariant
L	2.4750227405405	L(r)(E,1)/r!
Ω	0.28040033781114	Real period
R	1.2609638061785	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	10192bd2 40768k2 5733k2 15925h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 637c2

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	0	-	-3	-	-7	7	-6	-5	0	8	0	2	-7	-3	7	7	-3	-5	-14	-6	0	0	14

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Quadratic twists for elliptic curve 637c2

-4	8	-3	5	-7	-11	13
10192bd2	40768k2	5733k2	15925h2	637a2	77077n2	8281f2

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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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