Cremona's table of elliptic curves

1073 = 29 · 37

Field	Data	Notes
Atkin-Lehner	29- 37+	Signs for the Atkin-Lehner involutions
Class	1073a	Isogeny class
Conductor	1073	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	31117 = 292 · 37	Discriminant
Eigenvalues	0 -1 -4 -1 -3 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-45,132]	[a1,a2,a3,a4,a6]
Generators	[-2:14:1] [0:11:1]	Generators of the group modulo torsion
j	10303307776/31117	j-invariant
L	1.8618717098877	L(r)(E,1)/r!
Ω	3.7219479914832	Real period
R	0.25012059735209	Regulator
r	2	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17168l1 68672g1 9657a1 26825b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1073a1

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	-1	-4	-1	-3	-6	0	-4	-8	-	2	+	-11	-4	9	1	-2	4	-4	-15	1	8	-7	18	0

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Quadratic twists for elliptic curve 1073a1

-4	8	-3	5	-7	-11	29	37
17168l1	68672g1	9657a1	26825b1	52577d1	129833a1	31117b1	39701a1

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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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