Cremona's table of elliptic curves

1010 = 2 · 5 · 101

Field	Data	Notes
Atkin-Lehner	2- 5- 101+	Signs for the Atkin-Lehner involutions
Class	1010b	Isogeny class
Conductor	1010	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-80800 = -1 · 25 · 52 · 101	Discriminant
Eigenvalues	2- -2 5-  1 -6 -6 -1  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-15,25]	[a1,a2,a3,a4,a6]
Generators	[0:5:1]	Generators of the group modulo torsion
j	-374805361/80800	j-invariant
L	2.707601282598	L(r)(E,1)/r!
Ω	3.2754348688529	Real period
R	0.082663871852418	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	8080h1 32320f1 9090e1 5050b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1010b1

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
-	-2	-	1	-6	-6	-1	3	2	-5	-4	-12	-10	-1	10	9	0	-1	2	-4	-10	0	-14	6	-9

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Quadratic twists for elliptic curve 1010b1

-4	8	-3	5	-7	-11	101
8080h1	32320f1	9090e1	5050b1	49490n1	122210h1	102010b1

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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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