Cremona's table of elliptic curves

10140 = 2² · 3 · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	10140j	Isogeny class
Conductor	10140	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-6150193920 = -1 · 28 · 37 · 5 · 133	Discriminant
Eigenvalues	2- 3+ 5-  5 -3 13-  7  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-485,5745]	[a1,a2,a3,a4,a6]
j	-22478848/10935	j-invariant
L	2.5037014140878	L(r)(E,1)/r!
Ω	1.2518507070439	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40560dc1 30420p1 50700bi1 10140f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 10140j1

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
-	+	-	5	-3	-	7	4	-5	-10	-6	7	-5	10	4	3	4	-3	8	-11	-2	11	14	-7	-11

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Quadratic twists for elliptic curve 10140j1

-4	-3	5	13
40560dc1	30420p1	50700bi1	10140f1

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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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