Cremona's table of elliptic curves

629 = 17 · 37

Field	Data	Notes
Atkin-Lehner	17- 37-	Signs for the Atkin-Lehner involutions
Class	629d	Isogeny class
Conductor	629	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	220	Modular degree for the optimal curve
Δ	-1178847269 = -1 · 17 · 375	Discriminant
Eigenvalues	-1  0  3 -1 -5 -2 17-  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-171,1904]	[a1,a2,a3,a4,a6]
Generators	[16:47:1]	Generators of the group modulo torsion
j	-549957165057/1178847269	j-invariant
L	1.5536888030883	L(r)(E,1)/r!
Ω	1.3686582300295	Real period
R	0.22703824358764	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	10064h1 40256i1 5661h1 15725c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 629d1

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	3	-1	-5	-2	-	1	-6	1	4	-	-6	-11	-10	1	3	-5	-6	1	14	-8	6	0	-13

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Quadratic twists for elliptic curve 629d1

-4	8	-3	5	-7	-11	13	17	37
10064h1	40256i1	5661h1	15725c1	30821g1	76109f1	106301d1	10693d1	23273c1

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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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