Cremona's table of elliptic curves

18590 = 2 · 5 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	18590m	Isogeny class
Conductor	18590	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-45941954206720 = -1 · 210 · 5 · 11 · 138	Discriminant
Eigenvalues	2-  2 5+ -4 11- 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-23241,1392503]	[a1,a2,a3,a4,a6]
Generators	[57:478:1]	Generators of the group modulo torsion
j	-287626699801/9518080	j-invariant
L	9.0338299430487	L(r)(E,1)/r!
Ω	0.63510575757034	Real period
R	1.4224134855285	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	92950t1 1430c1	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 18590m1

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

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Quadratic twists for elliptic curve 18590m1

5	13
92950t1	1430c1

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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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