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	3312o	Isogeny class
Conductor	3312	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-2472394752 = -1 · 214 · 38 · 23	Discriminant
Eigenvalues	2- 3-  2  2 -6 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-219,2698]	[a1,a2,a3,a4,a6]
Generators	[-1:54:1]	Generators of the group modulo torsion
j	-389017/828	j-invariant
L	3.8641110557111	L(r)(E,1)/r!
Ω	1.2870177505242	Real period
R	0.75059397085572	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	414b1 13248bf1 1104i1 82800ek1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312o1

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

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Quadratic twists for elliptic curve 3312o1

-4	8	-3	5	-23
414b1	13248bf1	1104i1	82800ek1	76176ce1

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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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