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	12090k	Isogeny class
Conductor	12090	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	61600	Modular degree for the optimal curve
Δ	-651164313664800 = -1 · 25 · 37 · 52 · 13 · 315	Discriminant
Eigenvalues	2+ 3- 5+ -1  0 13+  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-25314,-1979564]	[a1,a2,a3,a4,a6]
Generators	[788:21228:1]	Generators of the group modulo torsion
j	-1793830388826762649/651164313664800	j-invariant
L	3.7726665134999	L(r)(E,1)/r!
Ω	0.18586971337574	Real period
R	0.28996244158504	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	96720bb1 36270bw1 60450cd1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12090k1

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	0	+	3	4	-2	2	-	-8	9	-8	-10	0	-15	15	-4	-6	-11	-3	6	6	-16

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Quadratic twists for elliptic curve 12090k1

-4	-3	5
96720bb1	36270bw1	60450cd1

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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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