Cremona's table of elliptic curves

12040 = 2³ · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 43-	Signs for the Atkin-Lehner involutions
Class	12040a	Isogeny class
Conductor	12040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2432	Modular degree for the optimal curve
Δ	385280 = 28 · 5 · 7 · 43	Discriminant
Eigenvalues	2+  0 5+ 7-  4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-503,-4342]	[a1,a2,a3,a4,a6]
Generators	[210793:2624544:1331]	Generators of the group modulo torsion
j	54977843664/1505	j-invariant
L	4.6605866099095	L(r)(E,1)/r!
Ω	1.0081108100634	Real period
R	9.2461792163828	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	24080a1 96320x1 108360bz1 60200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12040a1

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	+	-	4	6	2	-4	-4	-6	4	-6	-6	-	-8	-6	4	2	4	-8	2	-16	-4	-2	2

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Quadratic twists for elliptic curve 12040a1

-4	8	-3	5	-7
24080a1	96320x1	108360bz1	60200i1	84280n1

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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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