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	13800w	Isogeny class
Conductor	13800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	149040000000 = 210 · 34 · 57 · 23	Discriminant
Eigenvalues	2- 3- 5+ -4  4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-61408,5836688]	[a1,a2,a3,a4,a6]
Generators	[-97:3300:1]	Generators of the group modulo torsion
j	1600610497636/9315	j-invariant
L	5.0870991963944	L(r)(E,1)/r!
Ω	0.91526662220348	Real period
R	2.7790258450304	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	27600j4 110400s4 41400o4 2760a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13800w3

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	4	-6	2	4	+	-2	0	-2	2	0	0	6	-8	-2	16	-4	-10	0	-4	6	2

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Quadratic twists for elliptic curve 13800w3

-4	8	-3	5
27600j4	110400s4	41400o4	2760a3

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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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