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	738f	Isogeny class
Conductor	738	Conductor
∏ cp	44	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	-183638016 = -1 · 211 · 37 · 41	Discriminant
Eigenvalues	2- 3- -3 -2 -2  1 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-374,2949]	[a1,a2,a3,a4,a6]
Generators	[-7:75:1]	Generators of the group modulo torsion
j	-7916293657/251904	j-invariant
L	2.675140008053	L(r)(E,1)/r!
Ω	1.7902683596803	Real period
R	0.033960627309258	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5904n1 23616l1 246g1 18450h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 738f1

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	-2	1	-5	-1	-6	-8	3	-6	+	-4	12	14	-3	10	-7	3	1	12	-7	15	-10

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Quadratic twists for elliptic curve 738f1

-4	8	-3	5	-7	-11	13	41
5904n1	23616l1	246g1	18450h1	36162dc1	89298bh1	124722u1	30258v1

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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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