Cremona's table of elliptic curves

738 = 2 · 3² · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 41-	Signs for the Atkin-Lehner involutions
Class	738g	Isogeny class
Conductor	738	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-64321367112 = -1 · 23 · 314 · 412	Discriminant
Eigenvalues	2- 3-  2  2  4 -4  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-239,-12225]	[a1,a2,a3,a4,a6]
j	-2062933417/88232328	j-invariant
L	2.896620513252	L(r)(E,1)/r!
Ω	0.482770085542	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	5904r2 23616s2 246d2 18450o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 738g2

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	2	4	-4	2	-8	-4	8	4	2	-	4	2	-4	-12	-6	16	-6	-2	-14	-4	6	-2

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Quadratic twists for elliptic curve 738g2

-4	8	-3	5	-7	-11	13	41
5904r2	23616s2	246d2	18450o2	36162co2	89298s2	124722m2	30258r2

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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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