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	3330i	Isogeny class
Conductor	3330	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	235723844196000 = 25 · 316 · 53 · 372	Discriminant
Eigenvalues	2+ 3- 5-  0  2 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-190314,31995220]	[a1,a2,a3,a4,a6]
Generators	[221:722:1]	Generators of the group modulo torsion
j	1045706191321645729/323352324000	j-invariant
L	2.7605556269197	L(r)(E,1)/r!
Ω	0.54529585708325	Real period
R	0.84374857888638	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	26640bl2 106560br2 1110i2 16650cc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330i2

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

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Quadratic twists for elliptic curve 3330i2

-4	8	-3	5	37
26640bl2	106560br2	1110i2	16650cc2	123210cs2

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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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