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	64	Product of Tamagawa factors cp
Δ	653795140383 = 38 · 77 · 112	Discriminant
Eigenvalues	-1 3-  2 7- 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-221432,40087473]	[a1,a2,a3,a4,a6]
Generators	[-59:7306:1]	Generators of the group modulo torsion
j	10206027697760497/5557167	j-invariant
L	2.367874312483	L(r)(E,1)/r!
Ω	0.74717782781555	Real period
R	0.7922726773778	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25872bx6 103488cb6 4851o5 40425k6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617g5

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 1617g5

-4	8	-3	5	-7	-11
25872bx6	103488cb6	4851o5	40425k6	231a5	17787o5

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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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