Cremona's table of elliptic curves

10830 = 2 · 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	10830z	Isogeny class
Conductor	10830	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	300960	Modular degree for the optimal curve
Δ	-5342566979783884800 = -1 · 222 · 3 · 52 · 198	Discriminant
Eigenvalues	2- 3- 5+ -1  2 -3  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1847786,972996516]	[a1,a2,a3,a4,a6]
Generators	[2196:85542:1]	Generators of the group modulo torsion
j	-41081844659329/314572800	j-invariant
L	7.5177214144994	L(r)(E,1)/r!
Ω	0.24277688905101	Real period
R	0.23458754736066	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	86640bk1 32490o1 54150a1 10830b1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 10830z1

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	2	-3	4	+	-6	-10	1	-5	2	-5	0	-12	-2	5	-5	0	11	-11	2	0	-2

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Quadratic twists for elliptic curve 10830z1

-4	-3	5	-19
86640bk1	32490o1	54150a1	10830b1

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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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