Cremona's table of elliptic curves

10738 = 2 · 7 · 13 · 59

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+ 59+	Signs for the Atkin-Lehner involutions
Class	10738a	Isogeny class
Conductor	10738	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	2205359702 = 2 · 7 · 13 · 594	Discriminant
Eigenvalues	2+  0 -2 7+ -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1043,13031]	[a1,a2,a3,a4,a6]
Generators	[23:17:1]	Generators of the group modulo torsion
j	125548299739017/2205359702	j-invariant
L	2.1131742579235	L(r)(E,1)/r!
Ω	1.463739863975	Real period
R	2.8873631304745	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	85904v4 96642bq4 75166h4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 10738a3

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
+	0	-2	+	-4	+	2	-4	4	6	4	-6	10	4	-4	6	+	2	4	0	-6	16	-4	-6	10

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Quadratic twists for elliptic curve 10738a3

-4	-3	-7
85904v4	96642bq4	75166h4

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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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