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	13800b	Isogeny class
Conductor	13800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	230400	Modular degree for the optimal curve
Δ	-8980614787500000000 = -1 · 28 · 310 · 511 · 233	Discriminant
Eigenvalues	2+ 3+ 5+  3 -4  0 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,190367,140529637]	[a1,a2,a3,a4,a6]
Generators	[37:12150:1]	Generators of the group modulo torsion
j	190737654201344/2245153696875	j-invariant
L	4.1138747240107	L(r)(E,1)/r!
Ω	0.17067310483121	Real period
R	1.506489089215	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	27600ba1 110400de1 41400ca1 2760k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13800b1

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	-4	0	-3	-4	+	1	1	-1	3	12	10	9	-9	-10	-1	5	0	4	9	-8	10

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Quadratic twists for elliptic curve 13800b1

-4	8	-3	5
27600ba1	110400de1	41400ca1	2760k1

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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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