Cremona's table of elliptic curves

3468 = 2² · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Class	3468g	Isogeny class
Conductor	3468	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	756	Modular degree for the optimal curve
Δ	-10112688 = -1 · 24 · 37 · 172	Discriminant
Eigenvalues	2- 3- -2 -1  0 -3 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-249,1440]	[a1,a2,a3,a4,a6]
Generators	[3:27:1]	Generators of the group modulo torsion
j	-370720768/2187	j-invariant
L	3.5824018617342	L(r)(E,1)/r!
Ω	2.3023954861509	Real period
R	0.07409264215058	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872v1 55488h1 10404l1 86700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3468g1

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
-	-	-2	-1	0	-3	+	1	6	4	9	1	-8	-1	-8	-8	0	-11	-15	-6	-2	-16	-6	-14	3

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Quadratic twists for elliptic curve 3468g1

-4	8	-3	5	17
13872v1	55488h1	10404l1	86700d1	3468d1

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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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