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	18480x	Isogeny class
Conductor	18480	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	2766234240000 = 210 · 36 · 54 · 72 · 112	Discriminant
Eigenvalues	2+ 3- 5- 7+ 11+  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12640,536900]	[a1,a2,a3,a4,a6]
Generators	[-40:990:1]	Generators of the group modulo torsion
j	218121931923844/2701400625	j-invariant
L	6.3773846957394	L(r)(E,1)/r!
Ω	0.80963581079076	Real period
R	0.32820233342068	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9240i2 73920el2 55440k2 92400p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18480x2

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

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Quadratic twists for elliptic curve 18480x2

-4	8	-3	5	-7
9240i2	73920el2	55440k2	92400p2	129360l2

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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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