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	18720j	Isogeny class
Conductor	18720	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	3082757334037056000 = 29 · 310 · 53 · 138	Discriminant
Eigenvalues	2+ 3- 5+  4  0 13- -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1057683,-410068618]	[a1,a2,a3,a4,a6]
Generators	[1249:14742:1]	Generators of the group modulo torsion
j	350584567631475848/8259273550125	j-invariant
L	5.6839677184322	L(r)(E,1)/r!
Ω	0.1490849900463	Real period
R	2.3828554591021	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	18720l3 37440ff3 6240z3 93600dp3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18720j2

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	0	-	-2	8	-4	-6	-8	6	6	-4	-4	-6	-8	-10	4	-8	-14	0	-12	6	-6

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Quadratic twists for elliptic curve 18720j2

-4	8	-3	5
18720l3	37440ff3	6240z3	93600dp3

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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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