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	10010k	Isogeny class
Conductor	10010	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2396160	Modular degree for the optimal curve
Δ	-2.6460150167125E+25	Discriminant
Eigenvalues	2+  0 5- 7- 11+ 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1284241,247487120685]	[a1,a2,a3,a4,a6]
Generators	[2733695208783:-444295882176006:105823817]	Generators of the group modulo torsion
j	234241108436789946525879/26460150167125207212359680	j-invariant
L	3.3947944707437	L(r)(E,1)/r!
Ω	0.052911153611713	Real period
R	16.040070188492	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	80080bn1 90090dh1 50050bi1 70070d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010k1

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	-4	-2	8	-2	10	-4	-12	6	-12	-2	8	8	-2	-8	4	-6	2

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Quadratic twists for elliptic curve 10010k1

-4	-3	5	-7	-11
80080bn1	90090dh1	50050bi1	70070d1	110110cm1

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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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