Cremona's table of elliptic curves

629 = 17 · 37

Field	Data	Notes
Atkin-Lehner	17- 37-	Signs for the Atkin-Lehner involutions
Class	629c	Isogeny class
Conductor	629	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	3090277 = 174 · 37	Discriminant
Eigenvalues	0 -3  0  3 -1  0 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-40,48]	[a1,a2,a3,a4,a6]
Generators	[-6:8:1]	Generators of the group modulo torsion
j	7077888000/3090277	j-invariant
L	1.303779797179	L(r)(E,1)/r!
Ω	2.2765689140442	Real period
R	0.1431737678943	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	10064j1 40256k1 5661f1 15725b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 629c1

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	-3	0	3	-1	0	-	-2	-2	2	-8	-	3	-12	3	-11	-4	4	4	-3	-1	-2	1	6	0

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Quadratic twists for elliptic curve 629c1

-4	8	-3	5	-7	-11	13	17	37
10064j1	40256k1	5661f1	15725b1	30821e1	76109e1	106301c1	10693b1	23273a1

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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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