Cremona's table of elliptic curves

3417 = 3 · 17 · 67

Field	Data	Notes
Atkin-Lehner	3- 17- 67+	Signs for the Atkin-Lehner involutions
Class	3417g	Isogeny class
Conductor	3417	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	3417 = 3 · 17 · 67	Discriminant
Eigenvalues	1 3- -2  0  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-72,-239]	[a1,a2,a3,a4,a6]
Generators	[833296:11463713:4096]	Generators of the group modulo torsion
j	40459583737/3417	j-invariant
L	4.4673395795614	L(r)(E,1)/r!
Ω	1.6416993036509	Real period
R	10.884671924089	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	54672w1 10251e1 85425a1 58089a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3417g1

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	0	4	-2	-	4	-8	-2	8	-2	-6	-4	-4	-6	0	-6	+	0	-14	-8	0	-6	6

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Quadratic twists for elliptic curve 3417g1

-4	-3	5	17
54672w1	10251e1	85425a1	58089a1

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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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