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	3234f	Isogeny class
Conductor	3234	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-28174608 = -1 · 24 · 33 · 72 · 113	Discriminant
Eigenvalues	2+ 3+  0 7- 11-  4 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-60,288]	[a1,a2,a3,a4,a6]
Generators	[-4:24:1]	Generators of the group modulo torsion
j	-500313625/574992	j-invariant
L	2.2382146448734	L(r)(E,1)/r!
Ω	1.9058693793107	Real period
R	0.19572997929191	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	25872cj1 103488cv1 9702bs1 80850gs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234f1

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 3234f1

-4	8	-3	5	-7	-11
25872cj1	103488cv1	9702bs1	80850gs1	3234j1	35574bx1

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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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