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	13520y	Isogeny class
Conductor	13520	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	7140250000 = 24 · 56 · 134	Discriminant
Eigenvalues	2- -1 5-  1 -3 13+ -3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1070,13207]	[a1,a2,a3,a4,a6]
Generators	[9:65:1]	Generators of the group modulo torsion
j	296747776/15625	j-invariant
L	4.0462793332955	L(r)(E,1)/r!
Ω	1.3076231509282	Real period
R	0.1719098473705	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	3380f1 54080bz1 121680de1 67600bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520y1

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	-	1	-3	+	-3	7	3	3	4	-7	-9	-11	0	-6	3	11	7	3	2	-8	12	15	-7

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Quadratic twists for elliptic curve 13520y1

-4	8	-3	5	13
3380f1	54080bz1	121680de1	67600bp1	13520r1

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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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