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	12240cg	Isogeny class
Conductor	12240	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-3667534848000000000 = -1 · 219 · 36 · 59 · 173	Discriminant
Eigenvalues	2- 3- 5- -2  0 -1 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-956307,-371557294]	[a1,a2,a3,a4,a6]
Generators	[1337:27200:1]	Generators of the group modulo torsion
j	-32391289681150609/1228250000000	j-invariant
L	4.6132347471083	L(r)(E,1)/r!
Ω	0.076164928175435	Real period
R	0.5608242214699	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	1530g2 48960ew2 1360d2 61200et2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240cg2

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	-1	-	1	-6	3	-5	8	-6	10	-3	3	3	11	-2	9	11	-8	-12	-15	-7

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Quadratic twists for elliptic curve 12240cg2

-4	8	-3	5
1530g2	48960ew2	1360d2	61200et2

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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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