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	3234j	Isogeny class
Conductor	3234	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-3314714456592 = -1 · 24 · 33 · 78 · 113	Discriminant
Eigenvalues	2+ 3-  0 7+ 11- -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2966,-107656]	[a1,a2,a3,a4,a6]
Generators	[69:97:1]	Generators of the group modulo torsion
j	-500313625/574992	j-invariant
L	3.0288381364566	L(r)(E,1)/r!
Ω	0.30968621912307	Real period
R	1.6300575385806	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	25872bc1 103488a1 9702bm1 80850du1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234j1

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
+	-	0	+	-	-4	3	-1	-3	-9	2	-7	-6	11	-3	0	9	-10	-4	3	-4	-16	0	0	-1

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Quadratic twists for elliptic curve 3234j1

-4	8	-3	5	-7	-11
25872bc1	103488a1	9702bm1	80850du1	3234f1	35574ck1

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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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