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	273a	Isogeny class
Conductor	273	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-361179 = -1 · 34 · 73 · 13	Discriminant
Eigenvalues	-2 3+ -1 7- -2 13- -4  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-26,68]	[a1,a2,a3,a4,a6]
Generators	[11:31:1]	Generators of the group modulo torsion
j	-2019487744/361179	j-invariant
L	0.79370294255672	L(r)(E,1)/r!
Ω	2.9063397998432	Real period
R	0.045515608246011	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	4368w1 17472bf1 819f1 6825i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 273a1

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	-	-4	3	-9	-1	-5	-8	6	-9	-3	3	0	10	-2	12	5	-13	-11	1	1

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Quadratic twists for elliptic curve 273a1

-4	8	-3	5	-7	-11	13	17	-19
4368w1	17472bf1	819f1	6825i1	1911g1	33033a1	3549a1	78897j1	98553ba1

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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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