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	10010u	Isogeny class
Conductor	10010	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-2914912000 = -1 · 28 · 53 · 72 · 11 · 132	Discriminant
Eigenvalues	2-  0 5- 7+ 11- 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-457,4681]	[a1,a2,a3,a4,a6]
Generators	[1:64:1]	Generators of the group modulo torsion
j	-10533703412961/2914912000	j-invariant
L	6.6645115551792	L(r)(E,1)/r!
Ω	1.3561533777386	Real period
R	0.20476148643957	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	80080bu1 90090n1 50050q1 70070bm1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010u1

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	-	+	-	-	-2	-6	6	-6	4	-8	6	4	-6	2	-8	8	-8	8	6	-10	-16	-10	-14

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Quadratic twists for elliptic curve 10010u1

-4	-3	5	-7	-11
80080bu1	90090n1	50050q1	70070bm1	110110bg1

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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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