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	12240bh	Isogeny class
Conductor	12240	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-14343750000 = -1 · 24 · 33 · 59 · 17	Discriminant
Eigenvalues	2- 3+ 5-  1  3 -4 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,63,5759]	[a1,a2,a3,a4,a6]
Generators	[-2:75:1]	Generators of the group modulo torsion
j	64012032/33203125	j-invariant
L	5.1484723954205	L(r)(E,1)/r!
Ω	0.97353151107579	Real period
R	0.29380275926966	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	3060e1 48960dk1 12240bd2 61200dm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240bh1

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
-	+	-	1	3	-4	+	-5	-6	3	4	5	-9	10	-3	-3	12	-10	10	0	-1	4	-12	-12	-10

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Quadratic twists for elliptic curve 12240bh1

-4	8	-3	5
3060e1	48960dk1	12240bd2	61200dm1

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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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