Cremona's table of elliptic curves

13300 = 2² · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	13300k	Isogeny class
Conductor	13300	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	224640	Modular degree for the optimal curve
Δ	-1.23388671875E+19	Discriminant
Eigenvalues	2- -1 5+ 7-  3  5  1 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,56867,-168941863]	[a1,a2,a3,a4,a6]
Generators	[4004896:432801475:343]	Generators of the group modulo torsion
j	5084368707584/3084716796875	j-invariant
L	4.2962846873329	L(r)(E,1)/r!
Ω	0.10525869828193	Real period
R	10.204108442957	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	53200bu1 119700bc1 2660e1 93100t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300k1

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	+	-	3	5	1	+	4	-3	-8	-4	-8	-4	1	-12	-14	10	12	-8	6	-1	-4	-14	-1

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Quadratic twists for elliptic curve 13300k1

-4	-3	5	-7
53200bu1	119700bc1	2660e1	93100t1

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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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