Cremona's table of elliptic curves

1617 = 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	1617f	Isogeny class
Conductor	1617	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	210187945886590287 = 316 · 79 · 112	Discriminant
Eigenvalues	1 3-  0 7- 11+ -4  4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-174466,-17340319]	[a1,a2,a3,a4,a6]
Generators	[-167:2756:1]	Generators of the group modulo torsion
j	14553591673375/5208653241	j-invariant
L	3.8517784782432	L(r)(E,1)/r!
Ω	0.24053202753639	Real period
R	1.0008486493707	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872bu2 103488br2 4851s2 40425p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617f2

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	-	+	-4	4	-8	-8	2	-4	10	4	4	-12	6	-12	-12	4	0	-4	-8	-8	0	8

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Quadratic twists for elliptic curve 1617f2

-4	8	-3	5	-7	-11
25872bu2	103488br2	4851s2	40425p2	1617d2	17787s2

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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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