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	12240bx	Isogeny class
Conductor	12240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	1269043200 = 212 · 36 · 52 · 17	Discriminant
Eigenvalues	2- 3- 5-  2  2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1227,-16454]	[a1,a2,a3,a4,a6]
j	68417929/425	j-invariant
L	3.2278319138541	L(r)(E,1)/r!
Ω	0.80695797846351	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	765c1 48960ee1 1360g1 61200fs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240bx1

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
-	-	-	2	2	2	+	0	6	6	10	2	-10	-4	12	10	8	-14	-8	-2	-14	14	4	-6	2

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Quadratic twists for elliptic curve 12240bx1

-4	8	-3	5
765c1	48960ee1	1360g1	61200fs1

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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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