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	13520p	Isogeny class
Conductor	13520	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	8157307210000 = 24 · 54 · 138	Discriminant
Eigenvalues	2-  1 5+ -5  5 13+ -1  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5126,-34501]	[a1,a2,a3,a4,a6]
j	1141504/625	j-invariant
L	1.2055757337768	L(r)(E,1)/r!
Ω	0.60278786688841	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3380c1 54080dc1 121680fm1 67600bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520p1

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 13520p1

-4	8	-3	5	13
3380c1	54080dc1	121680fm1	67600bv1	13520x1

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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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