Cremona's table of elliptic curves

3312 = 2⁴ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 23-	Signs for the Atkin-Lehner involutions
Class	3312g	Isogeny class
Conductor	3312	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	5640305052672 = 210 · 39 · 234	Discriminant
Eigenvalues	2+ 3- -2  4 -4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6771,181474]	[a1,a2,a3,a4,a6]
Generators	[-85:378:1]	Generators of the group modulo torsion
j	45989074372/7555707	j-invariant
L	3.3228706398956	L(r)(E,1)/r!
Ω	0.72639343004476	Real period
R	2.2872389138286	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1656a3 13248bo3 1104c3 82800bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312g3

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

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Quadratic twists for elliptic curve 3312g3

-4	8	-3	5	-23
1656a3	13248bo3	1104c3	82800bc4	76176n4

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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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