Cremona's table of elliptic curves

444 = 2² · 3 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 37+	Signs for the Atkin-Lehner involutions
Class	444a	Isogeny class
Conductor	444	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1051392 = 28 · 3 · 372	Discriminant
Eigenvalues	2- 3+  0  0  4 -2  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-28,40]	[a1,a2,a3,a4,a6]
j	9826000/4107	j-invariant
L	1.2507526681308	L(r)(E,1)/r!
Ω	2.5015053362616	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1776h2 7104j2 1332c2 11100h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 444a2

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

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Quadratic twists for elliptic curve 444a2

-4	8	-3	5	-7	-11	13	17	37
1776h2	7104j2	1332c2	11100h2	21756l2	53724a2	75036b2	128316h2	16428a2

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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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