Cremona's table of elliptic curves

18480 = 2⁴ · 3 · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	18480m	Isogeny class
Conductor	18480	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	17285900163840000 = 211 · 32 · 54 · 7 · 118	Discriminant
Eigenvalues	2+ 3+ 5- 7+ 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1684880,842323872]	[a1,a2,a3,a4,a6]
Generators	[754:130:1]	Generators of the group modulo torsion
j	258286045443018193442/8440380939375	j-invariant
L	4.2600552189017	L(r)(E,1)/r!
Ω	0.3635197603638	Real period
R	2.929727406454	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	9240bj5 73920ge6 55440h6 92400cm6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18480m5

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	-6	4	0	6	0	-10	2	-4	0	6	4	-2	4	16	2	0	-12	-6	2

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Quadratic twists for elliptic curve 18480m5

-4	8	-3	5	-7
9240bj5	73920ge6	55440h6	92400cm6	129360cb6

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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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