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	10010h	Isogeny class
Conductor	10010	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3464060600 = 23 · 52 · 7 · 114 · 132	Discriminant
Eigenvalues	2+ -2 5- 7+ 11- 13+ -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-463,2538]	[a1,a2,a3,a4,a6]
Generators	[-18:80:1]	Generators of the group modulo torsion
j	10942526586601/3464060600	j-invariant
L	2.0639283188233	L(r)(E,1)/r!
Ω	1.3018177941357	Real period
R	0.39635506752954	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	80080bt2 90090cr2 50050bx2 70070o2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010h2

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

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Quadratic twists for elliptic curve 10010h2

-4	-3	5	-7	-11
80080bt2	90090cr2	50050bx2	70070o2	110110cw2

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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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