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	13520a	Isogeny class
Conductor	13520	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-3089157760000 = -1 · 210 · 54 · 136	Discriminant
Eigenvalues	2+  0 5+ -4  4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2197,74698]	[a1,a2,a3,a4,a6]
Generators	[91:1014:1]	Generators of the group modulo torsion
j	237276/625	j-invariant
L	3.5899319834389	L(r)(E,1)/r!
Ω	0.55994372725114	Real period
R	1.6028092684699	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6760g4 54080cw3 121680bw3 67600b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520a4

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
+	0	+	-4	4	+	2	4	-4	-2	-8	-6	6	8	4	6	-4	-2	8	0	6	0	-16	6	14

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Quadratic twists for elliptic curve 13520a4

-4	8	-3	5	13
6760g4	54080cw3	121680bw3	67600b3	80a4

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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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