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	12240bv	Isogeny class
Conductor	12240	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	215040	Modular degree for the optimal curve
Δ	666847516691250000 = 24 · 322 · 57 · 17	Discriminant
Eigenvalues	2- 3- 5-  0 -2  2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3964692,3038267351]	[a1,a2,a3,a4,a6]
j	590887175978458660864/57171426328125	j-invariant
L	1.9251632148023	L(r)(E,1)/r!
Ω	0.27502331640033	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	3060k1 48960eb1 4080s1 61200fe1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240bv1

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	-2	2	+	-8	4	-2	-2	6	-2	2	6	6	-8	10	2	2	-2	-10	-2	2	2

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Quadratic twists for elliptic curve 12240bv1

-4	8	-3	5
3060k1	48960eb1	4080s1	61200fe1

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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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