Cremona's table of elliptic curves

2093 = 7 · 13 · 23

Field	Data	Notes
Atkin-Lehner	7- 13- 23+	Signs for the Atkin-Lehner involutions
Class	2093f	Isogeny class
Conductor	2093	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	7776	Modular degree for the optimal curve
Δ	-585612268875179 = -1 · 74 · 139 · 23	Discriminant
Eigenvalues	0  1  3 7- -3 13- -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,16211,856569]	[a1,a2,a3,a4,a6]
Generators	[411:8781:1]	Generators of the group modulo torsion
j	471114356703100928/585612268875179	j-invariant
L	3.4091455862573	L(r)(E,1)/r!
Ω	0.34620175949925	Real period
R	2.461819945101	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	33488t1 18837r1 52325d1 14651e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2093f1

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
0	1	3	-	-3	-	-6	-7	+	-6	-4	2	6	-10	0	12	0	8	5	0	-16	-10	-15	6	17

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Quadratic twists for elliptic curve 2093f1

-4	-3	5	-7	13	-23
33488t1	18837r1	52325d1	14651e1	27209b1	48139f1

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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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