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	2400q	Isogeny class
Conductor	2400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	648000 = 26 · 34 · 53	Discriminant
Eigenvalues	2+ 3- 5- -4  0  4  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-538,4628]	[a1,a2,a3,a4,a6]
Generators	[8:30:1]	Generators of the group modulo torsion
j	2156689088/81	j-invariant
L	3.4460080586517	L(r)(E,1)/r!
Ω	2.6970374585861	Real period
R	0.31942530568877	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2400h1 4800ca2 7200ca1 2400z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400q1

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	0	4	0	-8	4	-6	-8	-4	6	4	-4	-12	0	-6	12	-16	0	-8	-12	-10	8

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Quadratic twists for elliptic curve 2400q1

-4	8	-3	5	-7
2400h1	4800ca2	7200ca1	2400z1	117600bl1

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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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