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	1617d	Isogeny class
Conductor	1617	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-32948443143 = -1 · 38 · 73 · 114	Discriminant
Eigenvalues	1 3+  0 7- 11+  4 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,675,5832]	[a1,a2,a3,a4,a6]
j	98931640625/96059601	j-invariant
L	1.5338441481626	L(r)(E,1)/r!
Ω	0.76692207408132	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872cv1 103488dr1 4851q1 40425cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617d1

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 1617d1

-4	8	-3	5	-7	-11
25872cv1	103488dr1	4851q1	40425cj1	1617f1	17787i1

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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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