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	3234g	Isogeny class
Conductor	3234	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	-104133351168 = -1 · 28 · 34 · 73 · 114	Discriminant
Eigenvalues	2+ 3+  0 7- 11- -4  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4505,115557]	[a1,a2,a3,a4,a6]
Generators	[-1:347:1]	Generators of the group modulo torsion
j	-29489309167375/303595776	j-invariant
L	2.1676848891193	L(r)(E,1)/r!
Ω	1.0651034040609	Real period
R	0.25439840874306	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	25872ck1 103488cu1 9702bu1 80850gp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234g1

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	4	0	0	2	-4	10	-12	4	4	-10	-4	4	4	-8	4	8	-16	8	-8

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Quadratic twists for elliptic curve 3234g1

-4	8	-3	5	-7	-11
25872ck1	103488cu1	9702bu1	80850gp1	3234m1	35574bw1

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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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