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	3330p	Isogeny class
Conductor	3330	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	-79920000 = -1 · 27 · 33 · 54 · 37	Discriminant
Eigenvalues	2- 3+ 5- -3  1 -1 -7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,103,121]	[a1,a2,a3,a4,a6]
Generators	[1:14:1]	Generators of the group modulo torsion
j	4516672077/2960000	j-invariant
L	4.910591881408	L(r)(E,1)/r!
Ω	1.2064666644263	Real period
R	0.072682605599492	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	26640w1 106560j1 3330a1 16650e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330p1

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	-7	-1	-3	0	-4	+	-6	4	-4	-7	2	-2	-8	12	1	-10	9	1	-12

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Quadratic twists for elliptic curve 3330p1

-4	8	-3	5	37
26640w1	106560j1	3330a1	16650e1	123210c1

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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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