Cremona's table of elliptic curves

10010 = 2 · 5 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 11+ 13-	Signs for the Atkin-Lehner involutions
Class	10010n	Isogeny class
Conductor	10010	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-881760880 = -1 · 24 · 5 · 72 · 113 · 132	Discriminant
Eigenvalues	2-  0 5+ 7+ 11+ 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,17,-1433]	[a1,a2,a3,a4,a6]
Generators	[25:106:1]	Generators of the group modulo torsion
j	573856191/881760880	j-invariant
L	5.8305573724961	L(r)(E,1)/r!
Ω	0.73380102221811	Real period
R	1.9864231569451	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	80080be1 90090bq1 50050k1 70070bw1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010n1

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

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Quadratic twists for elliptic curve 10010n1

-4	-3	5	-7	-11
80080be1	90090bq1	50050k1	70070bw1	110110m1

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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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