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	3234p	Isogeny class
Conductor	3234	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2984486028854022 = 2 · 34 · 712 · 113	Discriminant
Eigenvalues	2- 3+  0 7- 11+ -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-692518,221512829]	[a1,a2,a3,a4,a6]
Generators	[3886:-525:8]	Generators of the group modulo torsion
j	312196988566716625/25367712678	j-invariant
L	4.2560608972962	L(r)(E,1)/r!
Ω	0.43001477546391	Real period
R	4.9487379738344	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	25872ct4 103488dp4 9702u4 80850bx4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234p4

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

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Quadratic twists for elliptic curve 3234p4

-4	8	-3	5	-7	-11
25872ct4	103488dp4	9702u4	80850bx4	462g4	35574j4

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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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