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	240	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-10767236480000 = -1 · 210 · 54 · 76 · 11 · 13	Discriminant
Eigenvalues	2-  0 5- 7- 11- 13+  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1797,161021]	[a1,a2,a3,a4,a6]
Generators	[-9:424:1]	Generators of the group modulo torsion
j	-641418306895521/10767236480000	j-invariant
L	7.0112166571094	L(r)(E,1)/r!
Ω	0.60790325550335	Real period
R	0.19222402560596	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	80080bi1 90090w1 50050j1 70070bt1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10010y1

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 10010y1

-4	-3	5	-7	-11
80080bi1	90090w1	50050j1	70070bt1	110110y1

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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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