Cremona's table of elliptic curves

3330 = 2 · 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 37-	Signs for the Atkin-Lehner involutions
Class	3330o	Isogeny class
Conductor	3330	Conductor
∏ cp	180	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-599131788480000 = -1 · 29 · 33 · 54 · 375	Discriminant
Eigenvalues	2- 3+ 5+ -3 -1  1  1  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-62333,-6089019]	[a1,a2,a3,a4,a6]
Generators	[395:5352:1]	Generators of the group modulo torsion
j	-991990479802737267/22190066240000	j-invariant
L	4.4779777580297	L(r)(E,1)/r!
Ω	0.1508744806411	Real period
R	0.16488974215895	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	26640v1 106560p1 3330d1 16650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330o1

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
-	+	+	-3	-1	1	1	1	5	-4	-4	-	-10	-12	0	-9	14	2	-4	-8	-15	-14	-17	-7	-8

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Quadratic twists for elliptic curve 3330o1

-4	8	-3	5	37
26640v1	106560p1	3330d1	16650b1	123210n1

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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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