Cremona's table of elliptic curves

12090 = 2 · 3 · 5 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13- 31-	Signs for the Atkin-Lehner involutions
Class	12090bc	Isogeny class
Conductor	12090	Conductor
∏ cp	442	Product of Tamagawa factors cp
deg	2545920	Modular degree for the optimal curve
Δ	-692802881491968000 = -1 · 213 · 317 · 53 · 132 · 31	Discriminant
Eigenvalues	2- 3- 5+ -1 -5 13- -2  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-678646421,6804713564001]	[a1,a2,a3,a4,a6]
Generators	[15058:-11273:1]	Generators of the group modulo torsion
j	-34566419909754166339572971333329/692802881491968000	j-invariant
L	7.3628178684571	L(r)(E,1)/r!
Ω	0.14848516429319	Real period
R	0.11218601573904	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	96720bn1 36270bb1 60450g1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12090bc1

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
-	-	+	-1	-5	-	-2	1	9	-6	-	6	-2	-7	-6	5	-4	-2	4	11	-11	-11	6	-1	-12

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Quadratic twists for elliptic curve 12090bc1

-4	-3	5
96720bn1	36270bb1	60450g1

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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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