Cremona's table of elliptic curves

637 = 7² · 13

Field	Data	Notes
Atkin-Lehner	7- 13+	Signs for the Atkin-Lehner involutions
Class	637b	Isogeny class
Conductor	637	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-10706059 = -1 · 77 · 13	Discriminant
Eigenvalues	0  2  3 7-  0 13+  6  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-359,-2507]	[a1,a2,a3,a4,a6]
j	-43614208/91	j-invariant
L	2.192809362283	L(r)(E,1)/r!
Ω	0.54820234057076	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	10192bb1 40768bw1 5733f1 15925m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 637b1

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
0	2	3	-	0	+	6	7	3	-9	-5	2	6	-1	-3	-9	0	10	14	-6	-11	-1	-3	-15	1

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Quadratic twists for elliptic curve 637b1

-4	8	-3	5	-7	-11	13
10192bb1	40768bw1	5733f1	15925m1	91b1	77077v1	8281d1

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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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