Cremona's table of elliptic curves

1200 = 2⁴ · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5-	Signs for the Atkin-Lehner involutions
Class	1200n	Isogeny class
Conductor	1200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	281250000 = 24 · 32 · 59	Discriminant
Eigenvalues	2- 3+ 5- -4  4  0  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-333,-2088]	[a1,a2,a3,a4,a6]
Generators	[-12:6:1]	Generators of the group modulo torsion
j	131072/9	j-invariant
L	2.1644454514042	L(r)(E,1)/r!
Ω	1.1221538064486	Real period
R	1.9288313589153	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	300c1 4800cs1 3600br1 1200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200n1

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

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Quadratic twists for elliptic curve 1200n1

-4	8	-3	5	-7
300c1	4800cs1	3600br1	1200s1	58800jy1

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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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