Cremona's table of elliptic curves

637 = 7² · 13

Field	Data	Notes
Atkin-Lehner	7+ 13+	Signs for the Atkin-Lehner involutions
Class	637a	Isogeny class
Conductor	637	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-150659189317 = -1 · 74 · 137	Discriminant
Eigenvalues	1  0  0 7+ -3 13+  7 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,628,-17823]	[a1,a2,a3,a4,a6]
Generators	[104:1027:1]	Generators of the group modulo torsion
j	11397810375/62748517	j-invariant
L	2.4744038023472	L(r)(E,1)/r!
Ω	0.51577052346755	Real period
R	4.7974897551564	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	10192m2 40768f2 5733d2 15925d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 637a2

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 637a2

-4	8	-3	5	-7	-11	13
10192m2	40768f2	5733d2	15925d2	637c2	77077a2	8281b2

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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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