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	10010a	Isogeny class
Conductor	10010	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	96346250 = 2 · 54 · 72 · 112 · 13	Discriminant
Eigenvalues	2+  0 5+ 7+ 11+ 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-822155,-286726349]	[a1,a2,a3,a4,a6]
Generators	[12133:1326496:1]	Generators of the group modulo torsion
j	61458947171027474307849/96346250	j-invariant
L	2.4849147372067	L(r)(E,1)/r!
Ω	0.15854812278555	Real period
R	7.8364684915499	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	80080bd4 90090dm4 50050bt4 70070s4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010a3

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	+	+	+	+	-6	4	0	6	4	-6	2	8	8	-6	4	-2	4	12	-10	0	12	-6	-18

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Quadratic twists for elliptic curve 10010a3

-4	-3	5	-7	-11
80080bd4	90090dm4	50050bt4	70070s4	110110cf4

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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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