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	13120a	Isogeny class
Conductor	13120	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-15565141576908800 = -1 · 217 · 52 · 416	Discriminant
Eigenvalues	2+  0 5+  2 -4 -4  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-87628,11649648]	[a1,a2,a3,a4,a6]
Generators	[181:1311:1]	Generators of the group modulo torsion
j	-567730837600722/118752606025	j-invariant
L	4.1373851401702	L(r)(E,1)/r!
Ω	0.37605184585235	Real period
R	5.5010834088482	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	13120u2 1640a2 118080cs2 65600b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13120a2

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	-4	-4	2	8	4	-4	4	6	+	-4	-2	-12	4	-10	4	-6	6	6	4	18	10

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Quadratic twists for elliptic curve 13120a2

-4	8	-3	5
13120u2	1640a2	118080cs2	65600b2

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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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