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	2400bb	Isogeny class
Conductor	2400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	225000000 = 26 · 32 · 58	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-158,-312]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	438976/225	j-invariant
L	3.6059359293963	L(r)(E,1)/r!
Ω	1.422015497193	Real period
R	2.5357922867326	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2400r1 4800bh2 7200g1 480a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400bb1

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
-	-	+	0	-4	-2	2	-8	4	-6	0	-2	-6	4	-12	6	-12	14	-12	0	-2	8	-4	2	14

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Quadratic twists for elliptic curve 2400bb1

-4	8	-3	5	-7
2400r1	4800bh2	7200g1	480a1	117600ff1

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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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