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	10830h	Isogeny class
Conductor	10830	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-5792288868720 = -1 · 24 · 34 · 5 · 197	Discriminant
Eigenvalues	2+ 3+ 5-  4 -4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3617,-144411]	[a1,a2,a3,a4,a6]
Generators	[3670:76141:8]	Generators of the group modulo torsion
j	-111284641/123120	j-invariant
L	3.3246137764143	L(r)(E,1)/r!
Ω	0.29500787542826	Real period
R	2.8173940878595	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	86640eh1 32490bp1 54150ct1 570m1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 10830h1

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
+	+	-	4	-4	2	-2	-	-8	-6	-4	10	2	12	0	-6	0	-10	4	8	2	12	-8	-6	-18

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Quadratic twists for elliptic curve 10830h1

-4	-3	5	-19
86640eh1	32490bp1	54150ct1	570m1

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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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