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	3234r	Isogeny class
Conductor	3234	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-85077671052528 = -1 · 24 · 32 · 79 · 114	Discriminant
Eigenvalues	2- 3+ -2 7- 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4754,-463345]	[a1,a2,a3,a4,a6]
j	-100999381393/723148272	j-invariant
L	2.0383890743779	L(r)(E,1)/r!
Ω	0.25479863429724	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25872co1 103488dd1 9702p1 80850ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234r1

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	-	-	2	2	0	0	-2	-4	-2	10	4	-4	-2	12	2	12	8	-6	-8	8	14	14

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Quadratic twists for elliptic curve 3234r1

-4	8	-3	5	-7	-11
25872co1	103488dd1	9702p1	80850ck1	462f1	35574o1

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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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