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	12090l	Isogeny class
Conductor	12090	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	30950400 = 210 · 3 · 52 · 13 · 31	Discriminant
Eigenvalues	2+ 3- 5+  2 -6 13+  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-79,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	53540005609/30950400	j-invariant
L	3.8625882311955	L(r)(E,1)/r!
Ω	1.769440327582	Real period
R	2.1829434827417	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	96720bd1 36270bx1 60450ce1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12090l1

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	-6	+	6	-6	4	6	-	-6	-6	0	4	6	-4	-8	8	0	2	-8	-4	6	-12

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Quadratic twists for elliptic curve 12090l1

-4	-3	5
96720bd1	36270bx1	60450ce1

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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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