Cremona's table of elliptic curves

13120 = 2⁶ · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 41-	Signs for the Atkin-Lehner involutions
Class	13120bf	Isogeny class
Conductor	13120	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	17196646400 = 224 · 52 · 41	Discriminant
Eigenvalues	2-  0 5+  2 -6  2  8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-908,-8432]	[a1,a2,a3,a4,a6]
Generators	[-11:15:1]	Generators of the group modulo torsion
j	315821241/65600	j-invariant
L	4.1888641395291	L(r)(E,1)/r!
Ω	0.88244498395443	Real period
R	2.3734420931024	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	13120j1 3280l1 118080fh1 65600bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13120bf1

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

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Quadratic twists for elliptic curve 13120bf1

-4	8	-3	5
13120j1	3280l1	118080fh1	65600bu1

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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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