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	1200l	Isogeny class
Conductor	1200	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-300000000 = -1 · 28 · 3 · 58	Discriminant
Eigenvalues	2- 3+ 5-  1 -6  5 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-30333,2043537]	[a1,a2,a3,a4,a6]
Generators	[101:2:1]	Generators of the group modulo torsion
j	-30866268160/3	j-invariant
L	2.2840774806995	L(r)(E,1)/r!
Ω	1.327369763354	Real period
R	0.86037724519509	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	300b2 4800ci2 3600bl2 1200o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200l2

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	-6	5	-6	-5	6	-6	1	2	0	1	-6	-12	6	-13	-11	0	2	-8	6	0	-7

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Quadratic twists for elliptic curve 1200l2

-4	8	-3	5	-7
300b2	4800ci2	3600bl2	1200o2	58800ki2

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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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