Cremona's table of elliptic curves

13800 = 2³ · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	13800p	Isogeny class
Conductor	13800	Conductor
∏ cp	256	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-19801491660000000 = -1 · 28 · 316 · 57 · 23	Discriminant
Eigenvalues	2+ 3- 5+ -3 -2 -2  1  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7033,-6776437]	[a1,a2,a3,a4,a6]
Generators	[1103:-36450:1]	Generators of the group modulo torsion
j	-9619385344/4950372915	j-invariant
L	5.0683923727697	L(r)(E,1)/r!
Ω	0.17301692632687	Real period
R	0.11443046715977	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	27600d1 110400bi1 41400bq1 2760e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13800p1

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	-2	-2	1	6	-	3	-3	-3	-7	0	0	5	9	12	-3	3	-2	4	-7	-16	6

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Quadratic twists for elliptic curve 13800p1

-4	8	-3	5
27600d1	110400bi1	41400bq1	2760e1

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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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