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
deg	60	Modular degree for the optimal curve
Δ	-31213 = -1 · 74 · 13	Discriminant
Eigenvalues	1  0  0 7+ -3 13+  7 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-107,454]	[a1,a2,a3,a4,a6]
Generators	[6:-2:1]	Generators of the group modulo torsion
j	-56723625/13	j-invariant
L	2.4744038023472	L(r)(E,1)/r!
Ω	3.6103936642728	Real period
R	0.68535567930805	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	10192m1 40768f1 5733d1 15925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 637a1

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 637a1

-4	8	-3	5	-7	-11	13
10192m1	40768f1	5733d1	15925d1	637c1	77077a1	8281b1

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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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