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	10010c	Isogeny class
Conductor	10010	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6400	Modular degree for the optimal curve
Δ	394634240 = 210 · 5 · 72 · 112 · 13	Discriminant
Eigenvalues	2+  2 5+ 7- 11+ 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-238,948]	[a1,a2,a3,a4,a6]
Generators	[3:15:1]	Generators of the group modulo torsion
j	1500730351849/394634240	j-invariant
L	4.5313920483214	L(r)(E,1)/r!
Ω	1.5776417202195	Real period
R	1.4361283649659	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	80080y1 90090eb1 50050bg1 70070q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010c1

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	-2	6	-6	-4	-6	-12	8	8	-12	-10	-14	-4	10	-2	-12	16	-16	-18

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Quadratic twists for elliptic curve 10010c1

-4	-3	5	-7	-11
80080y1	90090eb1	50050bg1	70070q1	110110br1

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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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