Cremona's table of elliptic curves

273 = 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	273b	Isogeny class
Conductor	273	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-11870974573731 = -1 · 38 · 77 · 133	Discriminant
Eigenvalues	2 3-  1 7+ -2 13+  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,2540,-157433]	[a1,a2,a3,a4,a6]
j	1811564780171264/11870974573731	j-invariant
L	2.8527683183911	L(r)(E,1)/r!
Ω	0.35659603979889	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4368q1 17472c1 819d1 6825e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 273b1

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
2	-	1	+	-2	+	0	1	3	-5	9	0	2	-1	3	-9	0	-2	10	-12	15	11	3	-17	3

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Quadratic twists for elliptic curve 273b1

-4	8	-3	5	-7	-11	13	17	-19
4368q1	17472c1	819d1	6825e1	1911c1	33033bc1	3549d1	78897f1	98553i1

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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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