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	12240be	Isogeny class
Conductor	12240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	92160	Modular degree for the optimal curve
Δ	-18639706521600000 = -1 · 220 · 39 · 55 · 172	Discriminant
Eigenvalues	2- 3+ 5+  4 -2 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11043,6583842]	[a1,a2,a3,a4,a6]
Generators	[279:5022:1]	Generators of the group modulo torsion
j	-1847284083/231200000	j-invariant
L	4.6939353351526	L(r)(E,1)/r!
Ω	0.31728211529855	Real period
R	3.6985502088069	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	1530a1 48960dy1 12240bi1 61200di1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240be1

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

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Quadratic twists for elliptic curve 12240be1

-4	8	-3	5
1530a1	48960dy1	12240bi1	61200di1

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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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