Cremona's table of elliptic curves

3335 = 5 · 23 · 29

Field	Data	Notes
Atkin-Lehner	5+ 23+ 29+	Signs for the Atkin-Lehner involutions
Class	3335a	Isogeny class
Conductor	3335	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6560	Modular degree for the optimal curve
Δ	-6513671875 = -1 · 510 · 23 · 29	Discriminant
Eigenvalues	0  2 5+ -2  0  5 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-98021,11844826]	[a1,a2,a3,a4,a6]
Generators	[-122:4687:1]	Generators of the group modulo torsion
j	-104156296498930253824/6513671875	j-invariant
L	3.631106864209	L(r)(E,1)/r!
Ω	1.0089501270125	Real period
R	1.7994481426752	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53360m1 30015o1 16675c1 76705g1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 3335a1

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	+	-2	0	5	-3	5	+	+	-8	-5	2	-1	-6	2	5	6	-6	5	-10	-3	-2	-1	-10

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Quadratic twists for elliptic curve 3335a1

-4	-3	5	-23	29
53360m1	30015o1	16675c1	76705g1	96715a1

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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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