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	2400n	Isogeny class
Conductor	2400	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-69120000 = -1 · 212 · 33 · 54	Discriminant
Eigenvalues	2+ 3- 5-  1 -4 -3 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,67,363]	[a1,a2,a3,a4,a6]
Generators	[13:-60:1]	Generators of the group modulo torsion
j	12800/27	j-invariant
L	3.6582698296366	L(r)(E,1)/r!
Ω	1.3516171116613	Real period
R	0.15036596607437	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	2400x1 4800i1 7200bs1 2400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400n1

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
+	-	-	1	-4	-3	-4	-1	0	-8	1	2	2	-11	-2	-10	-6	11	9	6	-14	16	2	0	-11

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Quadratic twists for elliptic curve 2400n1

-4	8	-3	5	-7
2400x1	4800i1	7200bs1	2400s1	117600bz1

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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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