Cremona's table of elliptic curves

3354 = 2 · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 43+	Signs for the Atkin-Lehner involutions
Class	3354a	Isogeny class
Conductor	3354	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	3139344 = 24 · 33 · 132 · 43	Discriminant
Eigenvalues	2+ 3+ -2  2  6 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-41,-75]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	7916293657/3139344	j-invariant
L	2.1247116155688	L(r)(E,1)/r!
Ω	1.9460354454856	Real period
R	1.0918154756624	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	26832u1 107328ba1 10062j1 83850ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3354a1

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

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Quadratic twists for elliptic curve 3354a1

-4	8	-3	5	13
26832u1	107328ba1	10062j1	83850ck1	43602o1

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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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