Cremona's table of elliptic curves

330 = 2 · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11+	Signs for the Atkin-Lehner involutions
Class	330b	Isogeny class
Conductor	330	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-126720 = -1 · 28 · 32 · 5 · 11	Discriminant
Eigenvalues	2- 3- 5-  0 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,5,17]	[a1,a2,a3,a4,a6]
j	13651919/126720	j-invariant
L	2.418868993809	L(r)(E,1)/r!
Ω	2.418868993809	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2640q1 10560e1 990e1 1650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 330b1

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	-4	0	-2	0	-2	2	-12	8	6	-12	6	4	0	-6	-16	4	10	2

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Quadratic twists for elliptic curve 330b1

-4	8	-3	5	-7	-11	13	17	-19
2640q1	10560e1	990e1	1650a1	16170bj1	3630k1	55770z1	95370ca1	119130i1

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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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