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	2400d	Isogeny class
Conductor	2400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	262440000000 = 29 · 38 · 57	Discriminant
Eigenvalues	2+ 3+ 5+ -4  0  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2008,25012]	[a1,a2,a3,a4,a6]
Generators	[-44:162:1]	Generators of the group modulo torsion
j	111980168/32805	j-invariant
L	2.5088458290519	L(r)(E,1)/r!
Ω	0.91213456955652	Real period
R	1.3752607963712	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	2400k2 4800ch4 7200bp2 480h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400d3

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	2	6	0	-4	-2	8	-6	-6	12	-12	10	-8	-10	-12	-8	-10	-16	12	-6	-18

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Quadratic twists for elliptic curve 2400d3

-4	8	-3	5	-7
2400k2	4800ch4	7200bp2	480h3	117600cq3

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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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