Cremona's table of elliptic curves

13320 = 2³ · 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 37-	Signs for the Atkin-Lehner involutions
Class	13320b	Isogeny class
Conductor	13320	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-31968000 = -1 · 28 · 33 · 53 · 37	Discriminant
Eigenvalues	2+ 3+ 5-  0  0  3  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-132,644]	[a1,a2,a3,a4,a6]
Generators	[-2:30:1]	Generators of the group modulo torsion
j	-36799488/4625	j-invariant
L	5.2412623521015	L(r)(E,1)/r!
Ω	2.0187078845838	Real period
R	0.10818104640364	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	26640d1 106560a1 13320j1 66600z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13320b1

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	3	4	-8	0	-7	2	-	-10	1	11	-9	-5	-4	12	2	8	-10	1	-13	-18

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Quadratic twists for elliptic curve 13320b1

-4	8	-3	5
26640d1	106560a1	13320j1	66600z1

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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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