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	13120f	Isogeny class
Conductor	13120	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	8606720 = 210 · 5 · 412	Discriminant
Eigenvalues	2+ -2 5+  2  4 -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-61,99]	[a1,a2,a3,a4,a6]
Generators	[7:8:1]	Generators of the group modulo torsion
j	24918016/8405	j-invariant
L	3.2337688571699	L(r)(E,1)/r!
Ω	2.1366542801163	Real period
R	1.5134731375419	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	13120w1 1640b1 118080ct1 65600g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13120f1

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

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Quadratic twists for elliptic curve 13120f1

-4	8	-3	5
13120w1	1640b1	118080ct1	65600g1

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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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