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	3312n	Isogeny class
Conductor	3312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	170595237888 = 214 · 39 · 232	Discriminant
Eigenvalues	2- 3-  0 -2  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-82875,9182954]	[a1,a2,a3,a4,a6]
Generators	[143:506:1]	Generators of the group modulo torsion
j	21081759765625/57132	j-invariant
L	3.3188166708989	L(r)(E,1)/r!
Ω	0.88340463478323	Real period
R	1.878423850308	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	414a2 13248bd2 1104g2 82800ee2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312n2

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

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Quadratic twists for elliptic curve 3312n2

-4	8	-3	5	-23
414a2	13248bd2	1104g2	82800ee2	76176bs2

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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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