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	12240o	Isogeny class
Conductor	12240	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	5710694400 = 211 · 38 · 52 · 17	Discriminant
Eigenvalues	2+ 3- 5+  2  0  0 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6483,200882]	[a1,a2,a3,a4,a6]
Generators	[37:108:1]	Generators of the group modulo torsion
j	20183398562/3825	j-invariant
L	4.6415091825464	L(r)(E,1)/r!
Ω	1.310733208832	Real period
R	0.44264434891009	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	6120h2 48960fs2 4080g2 61200bk2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240o2

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	0	0	-	-4	0	-6	-4	10	-12	10	8	6	-6	6	-6	-2	12	-8	0	2	-16

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Quadratic twists for elliptic curve 12240o2

-4	8	-3	5
6120h2	48960fs2	4080g2	61200bk2

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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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