Cremona's table of elliptic curves

73 = Prime conductor

Field	Data	Notes
Atkin-Lehner	73-	Signs for the Atkin-Lehner involutions
Class	73a	Isogeny class
Conductor	73	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3	Modular degree for the optimal curve
Δ	-5329 = -1 · 732	Discriminant
Eigenvalues	1  0  2  2 -2 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,4,-3]	[a1,a2,a3,a4,a6]
j	6128487/5329	j-invariant
L	1.1826604672413	L(r)(E,1)/r!
Ω	2.3653209344827	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1168a2 4672a2 657d2 1825a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 73a1

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	0	2	2	-2	-6	2	8	4	2	-2	-6	6	-2	6	10	-6	-14	8	0	-	-4	-14	-6	-10

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Quadratic twists for elliptic curve 73a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	73
1168a2	4672a2	657d2	1825a2	3577a2	8833c2	12337a2	21097a2	26353b2	38617a2	61393a2	70153a2	99937d2	122713a2	5329a2

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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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