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	13800r	Isogeny class
Conductor	13800	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-1428300000000 = -1 · 28 · 33 · 58 · 232	Discriminant
Eigenvalues	2- 3+ 5- -3  2  1  8 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-833,-57963]	[a1,a2,a3,a4,a6]
Generators	[91:782:1]	Generators of the group modulo torsion
j	-640000/14283	j-invariant
L	3.6968419274466	L(r)(E,1)/r!
Ω	0.36847483001022	Real period
R	2.508205192295	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	27600bd1 110400ey1 41400ba1 13800o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13800r1

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	1	8	-5	+	0	-5	-2	0	-7	6	0	6	-7	13	-16	10	-8	-6	10	-13

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Quadratic twists for elliptic curve 13800r1

-4	8	-3	5
27600bd1	110400ey1	41400ba1	13800o1

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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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