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	438g	Isogeny class
Conductor	438	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	23652 = 22 · 34 · 73	Discriminant
Eigenvalues	2+ 3- -4  0  2  0 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	47045881/23652	j-invariant
L	1.4368065917803	L(r)(E,1)/r!
Ω	3.3567264352051	Real period
R	0.21401901815876	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	3504s1 14016p1 1314g1 10950q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 438g1

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	0	2	0	-6	-8	-8	-4	-4	2	10	-6	4	-8	14	-2	12	0	-	8	-18	6	-2

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Quadratic twists for elliptic curve 438g1

-4	8	-3	5	-7	-11	13	17	73
3504s1	14016p1	1314g1	10950q1	21462g1	52998r1	74022t1	126582f1	31974j1

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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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