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	3312k	Isogeny class
Conductor	3312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3656448 = 28 · 33 · 232	Discriminant
Eigenvalues	2- 3+  2 -2 -4 -2  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39,18]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	949104/529	j-invariant
L	3.5801117531509	L(r)(E,1)/r!
Ω	2.157827865067	Real period
R	1.6591275935904	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	828a2 13248z2 3312j2 82800ch2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312k2

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	-4	-2	2	2	-	4	0	2	0	2	-12	-2	-12	-14	-2	0	6	-6	-4	-18	6

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Quadratic twists for elliptic curve 3312k2

-4	8	-3	5	-23
828a2	13248z2	3312j2	82800ch2	76176bo2

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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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