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	2400a	Isogeny class
Conductor	2400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	120000000 = 29 · 3 · 57	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4008,99012]	[a1,a2,a3,a4,a6]
Generators	[137:1450:1]	Generators of the group modulo torsion
j	890277128/15	j-invariant
L	2.7207394653278	L(r)(E,1)/r!
Ω	1.7092573869466	Real period
R	3.1835339558639	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	2400ba2 4800q4 7200bf2 480g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2400a3

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	0	-2	-6	4	8	-2	-4	-10	2	-4	8	2	-8	-2	-12	-8	14	12	-4	-14	-2

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Quadratic twists for elliptic curve 2400a3

-4	8	-3	5	-7
2400ba2	4800q4	7200bf2	480g3	117600co4

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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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