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	3234k	Isogeny class
Conductor	3234	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-32286179772 = -1 · 22 · 34 · 77 · 112	Discriminant
Eigenvalues	2+ 3-  0 7- 11+  2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,219,8572]	[a1,a2,a3,a4,a6]
Generators	[-10:78:1]	Generators of the group modulo torsion
j	9938375/274428	j-invariant
L	3.0510887796829	L(r)(E,1)/r!
Ω	0.87900916696025	Real period
R	0.21694091017234	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	25872br1 103488bm1 9702bz1 80850dy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234k1

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

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Quadratic twists for elliptic curve 3234k1

-4	8	-3	5	-7	-11
25872br1	103488bm1	9702bz1	80850dy1	462a1	35574cx1

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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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