Cremona's table of elliptic curves

830 = 2 · 5 · 83

Field	Data	Notes
Atkin-Lehner	2- 5- 83+	Signs for the Atkin-Lehner involutions
Class	830c	Isogeny class
Conductor	830	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-2124800 = -1 · 210 · 52 · 83	Discriminant
Eigenvalues	2- -3 5- -3  3 -4 -1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3,69]	[a1,a2,a3,a4,a6]
Generators	[7:-24:1]	Generators of the group modulo torsion
j	4019679/2124800	j-invariant
L	2.2133179781819	L(r)(E,1)/r!
Ω	2.0301023316349	Real period
R	0.054512473181572	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	6640g1 26560d1 7470h1 4150d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 830c1

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
-	-3	-	-3	3	-4	-1	0	-8	-5	-5	9	-6	-10	-8	0	-11	-13	10	0	16	2	+	16	2

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Quadratic twists for elliptic curve 830c1

-4	8	-3	5	-7	-11	-83
6640g1	26560d1	7470h1	4150d1	40670t1	100430v1	68890c1

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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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