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	18720s	Isogeny class
Conductor	18720	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	143701646400000 = 29 · 312 · 55 · 132	Discriminant
Eigenvalues	2+ 3- 5- -2  0 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-298947,-62910214]	[a1,a2,a3,a4,a6]
Generators	[982:24300:1]	Generators of the group modulo torsion
j	7916055336451592/385003125	j-invariant
L	5.0849117916156	L(r)(E,1)/r!
Ω	0.20417486267802	Real period
R	2.4904690640759	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	18720r2 37440ek2 6240v2 93600eb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18720s2

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

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Quadratic twists for elliptic curve 18720s2

-4	8	-3	5
18720r2	37440ek2	6240v2	93600eb2

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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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