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	330d	Isogeny class
Conductor	330	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	448454983680000 = 228 · 35 · 54 · 11	Discriminant
Eigenvalues	2- 3+ 5+  4 11+  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-40266,2921559]	[a1,a2,a3,a4,a6]
j	7220044159551112609/448454983680000	j-invariant
L	1.816538214956	L(r)(E,1)/r!
Ω	0.51901091855886	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	2640u1 10560bg1 990g1 1650g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 330d1

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
-	+	+	4	+	2	2	4	-4	6	0	-10	-6	-12	-4	-6	-4	10	-12	-4	10	4	4	10	18

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Quadratic twists for elliptic curve 330d1

-4	8	-3	5	-7	-11	13	17	-19
2640u1	10560bg1	990g1	1650g1	16170ce1	3630c1	55770r1	95370dx1	119130m1

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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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