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	3234o	Isogeny class
Conductor	3234	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	1795315096092672 = 220 · 33 · 78 · 11	Discriminant
Eigenvalues	2+ 3- -2 7- 11- -2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31582,712016]	[a1,a2,a3,a4,a6]
j	29609739866953/15259926528	j-invariant
L	1.2433101855684	L(r)(E,1)/r!
Ω	0.4144367285228	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872bo1 103488s1 9702bv1 80850ek1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234o1

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	-6	8	4	2	-8	6	-6	8	-4	10	-4	14	-4	-4	14	-8	-4	14	-18

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Quadratic twists for elliptic curve 3234o1

-4	8	-3	5	-7	-11
25872bo1	103488s1	9702bv1	80850ek1	462b1	35574de1

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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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