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	4	Product of Tamagawa factors cp
Δ	-245059655680 = -1 · 211 · 5 · 7 · 434	Discriminant
Eigenvalues	2+  0 5+ 7-  4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,877,-21618]	[a1,a2,a3,a4,a6]
Generators	[40356:1014453:64]	Generators of the group modulo torsion
j	36424411182/119658035	j-invariant
L	4.6605866099095	L(r)(E,1)/r!
Ω	0.50405540503169	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	24080a3 96320x3 108360bz3 60200i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12040a4

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 12040a4

-4	8	-3	5	-7
24080a3	96320x3	108360bz3	60200i3	84280n3

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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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