Cremona's table of elliptic curves

2400 = 2⁵ · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+	Signs for the Atkin-Lehner involutions
Class	2400bd	Isogeny class
Conductor	2400	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-18139852800 = -1 · 212 · 311 · 52	Discriminant
Eigenvalues	2- 3- 5+ -3 -4  7 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-173,-6597]	[a1,a2,a3,a4,a6]
Generators	[49:324:1]	Generators of the group modulo torsion
j	-5624320/177147	j-invariant
L	3.4724002976367	L(r)(E,1)/r!
Ω	0.53368311253224	Real period
R	0.29574924418425	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	2400t1 4800bm1 7200n1 2400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400bd1

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	7	-4	1	-8	0	3	-2	-6	-11	6	-6	6	-1	-15	-6	-2	8	2	-16	-13

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Quadratic twists for elliptic curve 2400bd1

-4	8	-3	5	-7
2400t1	4800bm1	7200n1	2400g1	117600fi1

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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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