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	1617g	Isogeny class
Conductor	1617	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1588803803418447 = -1 · 32 · 77 · 118	Discriminant
Eigenvalues	-1 3-  2 7- 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1518,1917747]	[a1,a2,a3,a4,a6]
Generators	[186:2847:1]	Generators of the group modulo torsion
j	3288008303/13504609503	j-invariant
L	2.367874312483	L(r)(E,1)/r!
Ω	0.37358891390777	Real period
R	3.1690907095112	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	25872bx5 103488cb5 4851o6 40425k5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617g6

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	-	2	-	+	-6	-2	-4	0	-2	-8	6	-10	-4	8	6	-4	10	-12	0	-2	16	-4	-18	-2

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Quadratic twists for elliptic curve 1617g6

-4	8	-3	5	-7	-11
25872bx5	103488cb5	4851o6	40425k5	231a6	17787o6

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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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