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	10140h	Isogeny class
Conductor	10140	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-3244800 = -1 · 28 · 3 · 52 · 132	Discriminant
Eigenvalues	2- 3+ 5- -3 -6 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,35,25]	[a1,a2,a3,a4,a6]
Generators	[0:5:1]	Generators of the group modulo torsion
j	106496/75	j-invariant
L	3.3428825970369	L(r)(E,1)/r!
Ω	1.5948677138331	Real period
R	1.0480124991064	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	40560cx1 30420m1 50700bd1 10140c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 10140h1

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
-	+	-	-3	-6	+	6	0	2	8	-3	-6	-2	11	-12	-12	0	15	5	8	5	-15	8	6	1

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Quadratic twists for elliptic curve 10140h1

-4	-3	5	13
40560cx1	30420m1	50700bd1	10140c1

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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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