Cremona's table of elliptic curves

18720 = 2⁵ · 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	18720i	Isogeny class
Conductor	18720	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	76800	Modular degree for the optimal curve
Δ	-4981657075200000 = -1 · 212 · 311 · 55 · 133	Discriminant
Eigenvalues	2+ 3- 5+ -3 -3 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,42072,-706448]	[a1,a2,a3,a4,a6]
Generators	[212:4212:1]	Generators of the group modulo torsion
j	2758136205824/1668346875	j-invariant
L	3.8031560897971	L(r)(E,1)/r!
Ω	0.25097095485835	Real period
R	0.63140707722262	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	18720bi1 37440ch1 6240be1 93600dm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18720i1

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
+	-	+	-3	-3	-	3	-2	-1	8	-4	-5	7	-2	-4	11	-4	1	0	5	-2	3	-4	-7	5

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Quadratic twists for elliptic curve 18720i1

-4	8	-3	5
18720bi1	37440ch1	6240be1	93600dm1

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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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