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	18240w	Isogeny class
Conductor	18240	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	16634880 = 210 · 32 · 5 · 192	Discriminant
Eigenvalues	2+ 3+ 5- -2  0  4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-85,-203]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1]	Generators of the group modulo torsion
j	67108864/16245	j-invariant
L	4.2962378170618	L(r)(E,1)/r!
Ω	1.5984707682724	Real period
R	1.3438587374685	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	18240cp1 1140b1 54720bi1 91200dt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18240w1

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	0	4	-2	-	-6	2	0	4	2	-2	-6	12	4	-6	-12	0	-2	0	6	-14	8

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Quadratic twists for elliptic curve 18240w1

-4	8	-3	5
18240cp1	1140b1	54720bi1	91200dt1

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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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