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	13120bm	Isogeny class
Conductor	13120	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	268697600 = 218 · 52 · 41	Discriminant
Eigenvalues	2-  2 5- -2  6 -2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1345,19425]	[a1,a2,a3,a4,a6]
j	1027243729/1025	j-invariant
L	3.4672131835932	L(r)(E,1)/r!
Ω	1.7336065917966	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13120t1 3280i1 118080ek1 65600cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13120bm1

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	6	-2	2	-6	4	-10	0	6	-	-4	2	14	12	10	-2	2	6	2	0	10	10

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Quadratic twists for elliptic curve 13120bm1

-4	8	-3	5
13120t1	3280i1	118080ek1	65600cc1

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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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