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	2400x	Isogeny class
Conductor	2400	Conductor
∏ cp	6	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	[7:20:1]	Generators of the group modulo torsion
j	12800/27	j-invariant
L	2.7090845062711	L(r)(E,1)/r!
Ω	1.0147862762806	Real period
R	0.44493515031893	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	2400n1 4800bb1 7200t1 2400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400x1

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 2400x1

-4	8	-3	5	-7
2400n1	4800bb1	7200t1	2400j1	117600ia1

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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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