Cremona's table of elliptic curves

1320 = 2³ · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	1320a	Isogeny class
Conductor	1320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	87120 = 24 · 32 · 5 · 112	Discriminant
Eigenvalues	2+ 3+ 5+  2 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11,0]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	10061824/5445	j-invariant
L	2.2948151091053	L(r)(E,1)/r!
Ω	2.773112663085	Real period
R	0.41376160796734	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	2640i1 10560bc1 3960r1 6600ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1320a1

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
+	+	+	2	+	-4	0	-4	4	6	-8	-10	-6	6	12	-10	4	-14	-8	-8	-4	0	-14	-18	-10

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Quadratic twists for elliptic curve 1320a1

-4	8	-3	5	-7	-11
2640i1	10560bc1	3960r1	6600ba1	64680be1	14520bb1

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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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