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	13120be	Isogeny class
Conductor	13120	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	4198400 = 212 · 52 · 41	Discriminant
Eigenvalues	2-  0 5+  2 -2 -2  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,192]	[a1,a2,a3,a4,a6]
Generators	[-4:20:1]	Generators of the group modulo torsion
j	8489664/1025	j-invariant
L	4.2517106293123	L(r)(E,1)/r!
Ω	2.3800339059351	Real period
R	0.89320379401104	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	13120bg1 6560e1 118080fe1 65600bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13120be1

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	-2	-2	0	6	-4	4	0	6	-	-4	-6	10	-4	-2	16	-8	2	-4	-12	6	-12

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Quadratic twists for elliptic curve 13120be1

-4	8	-3	5
13120bg1	6560e1	118080fe1	65600bt1

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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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