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	738j	Isogeny class
Conductor	738	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-1614006 = -1 · 2 · 39 · 41	Discriminant
Eigenvalues	2- 3- -3  2  6 -1 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-14,-61]	[a1,a2,a3,a4,a6]
j	-389017/2214	j-invariant
L	2.2263556127011	L(r)(E,1)/r!
Ω	1.1131778063506	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5904v1 23616x1 246f1 18450q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 738j1

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
-	-	-3	2	6	-1	-3	5	6	0	-1	2	-	8	12	-6	9	-10	-13	-15	-7	-4	-3	-15	2

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Quadratic twists for elliptic curve 738j1

-4	8	-3	5	-7	-11	13	41
5904v1	23616x1	246f1	18450q1	36162cs1	89298z1	124722o1	30258w1

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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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