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	10010m	Isogeny class
Conductor	10010	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	146356560350 = 2 · 52 · 7 · 114 · 134	Discriminant
Eigenvalues	2-  0 5+ 7+ 11+ 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2293,38607]	[a1,a2,a3,a4,a6]
j	1332779492447649/146356560350	j-invariant
L	1.9969614559533	L(r)(E,1)/r!
Ω	0.99848072797663	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	80080bc4 90090bp4 50050p4 70070ce4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010m3

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	-8	0	2	0	2	-6	-12	0	14	12	2	-12	12	2	-4	16	14	-10

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Quadratic twists for elliptic curve 10010m3

-4	-3	5	-7	-11
80080bc4	90090bp4	50050p4	70070ce4	110110u4

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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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