Cremona's table of elliptic curves

12240 = 2⁴ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	12240k	Isogeny class
Conductor	12240	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	-1087904013750000 = -1 · 24 · 311 · 57 · 173	Discriminant
Eigenvalues	2+ 3- 5+  3 -1 -6 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-25563,2234513]	[a1,a2,a3,a4,a6]
j	-158384129218816/93270234375	j-invariant
L	1.8179183303773	L(r)(E,1)/r!
Ω	0.45447958259432	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6120f1 48960fj1 4080j1 61200by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240k1

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	-1	-6	+	1	6	5	2	-11	9	0	5	3	-12	-10	-4	-4	3	2	12	-4	14

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Quadratic twists for elliptic curve 12240k1

-4	8	-3	5
6120f1	48960fj1	4080j1	61200by1

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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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