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	12040c	Isogeny class
Conductor	12040	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-1396270131200 = -1 · 211 · 52 · 73 · 433	Discriminant
Eigenvalues	2+  3 5- 7- -5 -2 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7027,-233746]	[a1,a2,a3,a4,a6]
Generators	[3126:19180:27]	Generators of the group modulo torsion
j	-18737153748882/681772525	j-invariant
L	8.1142435543166	L(r)(E,1)/r!
Ω	0.26016570323259	Real period
R	5.1981253059723	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	24080d1 96320n1 108360bj1 60200m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12040c1

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	-	-	-5	-2	-4	-5	4	-5	-5	3	-6	+	-8	-12	-10	4	-1	-3	6	6	-10	-15	-8

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Quadratic twists for elliptic curve 12040c1

-4	8	-3	5	-7
24080d1	96320n1	108360bj1	60200m1	84280f1

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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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