Cremona's table of elliptic curves

13520 = 2⁴ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 13-	Signs for the Atkin-Lehner involutions
Class	13520bg	Isogeny class
Conductor	13520	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	134784	Modular degree for the optimal curve
Δ	347488235454464000 = 218 · 53 · 139	Discriminant
Eigenvalues	2- -2 5-  0  0 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-185280,11682100]	[a1,a2,a3,a4,a6]
j	16194277/8000	j-invariant
L	1.6142046304536	L(r)(E,1)/r!
Ω	0.2690341050756	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	1690i1 54080cp1 121680ef1 67600cs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520bg1

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	-	0	0	-	6	0	0	6	6	6	0	-10	12	0	12	10	-12	-6	-6	8	12	-12	-18

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Quadratic twists for elliptic curve 13520bg1

-4	8	-3	5	13
1690i1	54080cp1	121680ef1	67600cs1	13520v1

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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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