Cremona's table of elliptic curves

18240 = 2⁶ · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	18240u	Isogeny class
Conductor	18240	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-27724800 = -1 · 210 · 3 · 52 · 192	Discriminant
Eigenvalues	2+ 3+ 5- -4 -2 -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,75,-75]	[a1,a2,a3,a4,a6]
Generators	[5:20:1] [37:228:1]	Generators of the group modulo torsion
j	44957696/27075	j-invariant
L	5.9794798551249	L(r)(E,1)/r!
Ω	1.2248984520694	Real period
R	2.4408063562433	Regulator
r	2	Rank of the group of rational points
S	0.99999999999967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	18240cz1 1140d1 54720ba1 91200dj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18240u1

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	-2	+	6	-8	-8	-10	-4	-4	6	-12	8	-2	-4	12	-10	-8	-2	-12	-14

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Quadratic twists for elliptic curve 18240u1

-4	8	-3	5
18240cz1	1140d1	54720ba1	91200dj1

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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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