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	10140f	Isogeny class
Conductor	10140	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	131040	Modular degree for the optimal curve
Δ	-29685811364801280 = -1 · 28 · 37 · 5 · 139	Discriminant
Eigenvalues	2- 3+ 5+ -5  3 13-  7 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-82021,12293761]	[a1,a2,a3,a4,a6]
Generators	[-225:4394:1]	Generators of the group modulo torsion
j	-22478848/10935	j-invariant
L	2.8416947540278	L(r)(E,1)/r!
Ω	0.34720091642097	Real period
R	1.3640971839018	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40560cp1 30420z1 50700bh1 10140j1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 10140f1

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 10140f1

-4	-3	5	13
40560cp1	30420z1	50700bh1	10140j1

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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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