Cremona's table of elliptic curves

438 = 2 · 3 · 73

Field	Data	Notes
Atkin-Lehner	2- 3+ 73-	Signs for the Atkin-Lehner involutions
Class	438f	Isogeny class
Conductor	438	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6906384 = 24 · 34 · 732	Discriminant
Eigenvalues	2- 3+ -2 -4  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-99,-399]	[a1,a2,a3,a4,a6]
Generators	[-7:6:1]	Generators of the group modulo torsion
j	107375065777/6906384	j-invariant
L	2.0220564890908	L(r)(E,1)/r!
Ω	1.519555930282	Real period
R	1.3306890840902	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	3504x2 14016bc2 1314c2 10950j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 438f2

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

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Quadratic twists for elliptic curve 438f2

-4	8	-3	5	-7	-11	13	17	73
3504x2	14016bc2	1314c2	10950j2	21462bb2	52998b2	74022b2	126582bb2	31974k2

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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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