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	32	Product of Tamagawa factors cp
deg	8960	Modular degree for the optimal curve
Δ	-3876351387330807 = -1 · 38 · 79 · 114	Discriminant
Eigenvalues	1 3-  0 7- 11+ -4  4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,33049,-1901203]	[a1,a2,a3,a4,a6]
Generators	[537:12799:1]	Generators of the group modulo torsion
j	98931640625/96059601	j-invariant
L	3.8517784782432	L(r)(E,1)/r!
Ω	0.24053202753639	Real period
R	2.0016972987415	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	25872bu1 103488br1 4851s1 40425p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617f1

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 1617f1

-4	8	-3	5	-7	-11
25872bu1	103488br1	4851s1	40425p1	1617d1	17787s1

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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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