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	13520x	Isogeny class
Conductor	13520	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	1690000 = 24 · 54 · 132	Discriminant
Eigenvalues	2-  1 5-  5 -5 13+ -1 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-30,-25]	[a1,a2,a3,a4,a6]
Generators	[-5:5:1]	Generators of the group modulo torsion
j	1141504/625	j-invariant
L	6.442694503631	L(r)(E,1)/r!
Ω	2.1733825622937	Real period
R	0.74109070986927	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3380g1 54080ce1 121680ed1 67600bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520x1

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
-	1	-	5	-5	+	-1	-3	-3	-1	0	-7	5	-5	12	2	-11	-13	3	13	2	4	12	-7	-11

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Quadratic twists for elliptic curve 13520x1

-4	8	-3	5	13
3380g1	54080ce1	121680ed1	67600bw1	13520p1

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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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