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	13800f	Isogeny class
Conductor	13800	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	1482933427200 = 210 · 32 · 52 · 235	Discriminant
Eigenvalues	2+ 3+ 5+ -3 -3 -7 -6  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2968,22012]	[a1,a2,a3,a4,a6]
Generators	[-22:276:1] [1:138:1]	Generators of the group modulo torsion
j	112985250820/57927087	j-invariant
L	5.3228058479917	L(r)(E,1)/r!
Ω	0.74948577370831	Real period
R	0.35509719028122	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27600u1 110400ef1 41400br1 13800z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13800f1

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	-3	-7	-6	3	-	3	0	0	-3	-3	-10	0	-6	-8	-12	6	-9	-13	-9	-14	12

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Quadratic twists for elliptic curve 13800f1

-4	8	-3	5
27600u1	110400ef1	41400br1	13800z1

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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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