Cremona's table of elliptic curves

3234 = 2 · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	3234v	Isogeny class
Conductor	3234	Conductor
∏ cp	336	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-495709175808 = -1 · 214 · 36 · 73 · 112	Discriminant
Eigenvalues	2- 3- -2 7- 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3179,76593]	[a1,a2,a3,a4,a6]
Generators	[22:121:1]	Generators of the group modulo torsion
j	-10358806345399/1445216256	j-invariant
L	5.1654962369442	L(r)(E,1)/r!
Ω	0.90101396661303	Real period
R	0.068249777583276	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	25872bp1 103488w1 9702q1 80850u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234v1

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	-	-	-4	-6	-2	0	-6	-2	2	2	-12	6	10	-8	-4	0	-8	-6	12	-6	12	0

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Quadratic twists for elliptic curve 3234v1

-4	8	-3	5	-7	-11
25872bp1	103488w1	9702q1	80850u1	3234q1	35574bi1

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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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