Cremona's table of elliptic curves

629 = 17 · 37

Field	Data	Notes
Atkin-Lehner	17- 37+	Signs for the Atkin-Lehner involutions
Class	629b	Isogeny class
Conductor	629	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	14638717 = 172 · 373	Discriminant
Eigenvalues	2  3 -2  1 -3  4 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-211,1165]	[a1,a2,a3,a4,a6]
j	1038893617152/14638717	j-invariant
L	4.4533939179586	L(r)(E,1)/r!
Ω	2.2266969589793	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	10064g1 40256t1 5661e1 15725e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 629b1

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	3	-2	1	-3	4	-	2	-2	-6	-2	+	-3	4	3	-3	0	2	4	-13	9	0	5	16	8

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Quadratic twists for elliptic curve 629b1

-4	8	-3	5	-7	-11	13	17	37
10064g1	40256t1	5661e1	15725e1	30821a1	76109d1	106301e1	10693f1	23273d1

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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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