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	10010y	Isogeny class
Conductor	10010	Conductor
∏ cp	480	Product of Tamagawa factors cp
Δ	87675087500000 = 25 · 58 · 73 · 112 · 132	Discriminant
Eigenvalues	2-  0 5- 7- 11- 13+  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-56677,5188029]	[a1,a2,a3,a4,a6]
Generators	[537:-11644:1]	Generators of the group modulo torsion
j	20134325779217044641/87675087500000	j-invariant
L	7.0112166571094	L(r)(E,1)/r!
Ω	0.60790325550335	Real period
R	0.09611201280298	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	80080bi2 90090w2 50050j2 70070bt2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010y2

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	-	-	-	+	0	-8	4	4	0	-8	-10	-8	-4	-10	6	6	-4	-10	6	-10	16	0	-8

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Quadratic twists for elliptic curve 10010y2

-4	-3	5	-7	-11
80080bi2	90090w2	50050j2	70070bt2	110110y2

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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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