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	12090n	Isogeny class
Conductor	12090	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	30240	Modular degree for the optimal curve
Δ	-19065601152000 = -1 · 210 · 37 · 53 · 133 · 31	Discriminant
Eigenvalues	2+ 3- 5+ -2 -1 13- -4  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,5806,-122524]	[a1,a2,a3,a4,a6]
Generators	[141:-1943:1]	Generators of the group modulo torsion
j	21650220735939431/19065601152000	j-invariant
L	3.4361903813445	L(r)(E,1)/r!
Ω	0.37778077954015	Real period
R	0.21656489988258	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	96720bt1 36270ca1 60450br1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12090n1

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	-1	-	-4	1	1	-5	+	0	7	-4	11	12	14	10	0	-6	-10	-8	4	12	-6

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Quadratic twists for elliptic curve 12090n1

-4	-3	5
96720bt1	36270ca1	60450br1

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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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