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	3330c	Isogeny class
Conductor	3330	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-1165233600 = -1 · 26 · 39 · 52 · 37	Discriminant
Eigenvalues	2+ 3+ 5-  0 -2 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-339,-2827]	[a1,a2,a3,a4,a6]
Generators	[49:286:1]	Generators of the group modulo torsion
j	-219256227/59200	j-invariant
L	2.6803134528988	L(r)(E,1)/r!
Ω	0.54851473004528	Real period
R	2.443246558463	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	26640z1 106560b1 3330n1 16650bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330c1

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	2	-8	4	10	2	-	-8	-6	-6	0	4	-4	-16	-4	6	10	-16	-2	-8

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Quadratic twists for elliptic curve 3330c1

-4	8	-3	5	37
26640z1	106560b1	3330n1	16650bn1	123210bx1

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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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