Cremona's table of elliptic curves

637 = 7² · 13

Field	Data	Notes
Atkin-Lehner	7- 13-	Signs for the Atkin-Lehner involutions
Class	637d	Isogeny class
Conductor	637	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-10706059 = -1 · 77 · 13	Discriminant
Eigenvalues	-2  0  3 7- -6 13- -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,49,-86]	[a1,a2,a3,a4,a6]
Generators	[7:24:1]	Generators of the group modulo torsion
j	110592/91	j-invariant
L	1.2952727036516	L(r)(E,1)/r!
Ω	1.261847555736	Real period
R	0.51324452694926	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	10192bh1 40768o1 5733l1 15925j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 637d1

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
-2	0	3	-	-6	-	-4	-5	3	-5	3	-4	6	-1	-7	-9	-8	10	-6	-8	13	3	-15	-3	-7

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Quadratic twists for elliptic curve 637d1

-4	8	-3	5	-7	-11	13
10192bh1	40768o1	5733l1	15925j1	91a1	77077r1	8281i1

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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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