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	12240v	Isogeny class
Conductor	12240	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	614345796000000 = 28 · 312 · 56 · 172	Discriminant
Eigenvalues	2+ 3- 5-  0 -4  6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-41367,-3010826]	[a1,a2,a3,a4,a6]
j	41948679809104/3291890625	j-invariant
L	2.0185618469827	L(r)(E,1)/r!
Ω	0.33642697449711	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6120m2 48960er2 4080l2 61200bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240v2

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	-	-4	-8	6	-4	2	-6	4	4	-10	12	6	4	0	14	4	16	-10	6

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Quadratic twists for elliptic curve 12240v2

-4	8	-3	5
6120m2	48960er2	4080l2	61200bd2

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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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