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	32	Product of Tamagawa factors cp
Δ	6836598566721 = 34 · 78 · 114	Discriminant
Eigenvalues	-1 3-  2 7- 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-13917,618120]	[a1,a2,a3,a4,a6]
Generators	[-15:915:1]	Generators of the group modulo torsion
j	2533811507137/58110129	j-invariant
L	2.367874312483	L(r)(E,1)/r!
Ω	0.74717782781555	Real period
R	1.5845453547556	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	25872bx4 103488cb4 4851o3 40425k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617g3

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 1617g3

-4	8	-3	5	-7	-11
25872bx4	103488cb4	4851o3	40425k4	231a3	17787o3

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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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