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	10830i	Isogeny class
Conductor	10830	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	49248	Modular degree for the optimal curve
Δ	-45855620210700 = -1 · 22 · 33 · 52 · 198	Discriminant
Eigenvalues	2+ 3- 5+ -1  6  5  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13004,656102]	[a1,a2,a3,a4,a6]
j	-14317849/2700	j-invariant
L	2.4517026552284	L(r)(E,1)/r!
Ω	0.61292566380709	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	86640bm1 32490bq1 54150bm1 10830t1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 10830i1

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	6	5	0	+	6	6	5	11	6	-1	12	-12	6	-7	-1	0	-1	-7	-6	-12	14

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Quadratic twists for elliptic curve 10830i1

-4	-3	5	-19
86640bm1	32490bq1	54150bm1	10830t1

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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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