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	13520n	Isogeny class
Conductor	13520	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	328982944808960 = 220 · 5 · 137	Discriminant
Eigenvalues	2-  0 5+  0  0 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-18083,338338]	[a1,a2,a3,a4,a6]
j	33076161/16640	j-invariant
L	0.95857248120721	L(r)(E,1)/r!
Ω	0.4792862406036	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	1690a1 54080cs1 121680em1 67600be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520n1

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	+	0	0	+	2	-8	4	-2	-4	-6	-10	0	8	6	8	-2	4	-12	-10	8	12	-10	14

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Quadratic twists for elliptic curve 13520n1

-4	8	-3	5	13
1690a1	54080cs1	121680em1	67600be1	1040f1

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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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