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	738d	Isogeny class
Conductor	738	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-522937944 = -1 · 23 · 313 · 41	Discriminant
Eigenvalues	2+ 3- -1  2 -2 -7 -7  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2430,46732]	[a1,a2,a3,a4,a6]
Generators	[41:101:1]	Generators of the group modulo torsion
j	-2177286259681/717336	j-invariant
L	1.6730284056024	L(r)(E,1)/r!
Ω	1.6152729785813	Real period
R	0.25893895765405	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	5904p1 23616o1 246a1 18450bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 738d1

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
+	-	-1	2	-2	-7	-7	7	2	8	-5	-10	-	-8	-4	2	-9	6	1	-15	1	-8	11	-3	10

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Quadratic twists for elliptic curve 738d1

-4	8	-3	5	-7	-11	13	41
5904p1	23616o1	246a1	18450bw1	36162q1	89298cc1	124722bm1	30258e1

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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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