Cremona's table of elliptic curves

272 = 2⁴ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	272a	Isogeny class
Conductor	272	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	591872 = 211 · 172	Discriminant
Eigenvalues	2+ -2  0  0 -2 -6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-48,-140]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1]	Generators of the group modulo torsion
j	6097250/289	j-invariant
L	1.2387792395146	L(r)(E,1)/r!
Ω	1.8159830187127	Real period
R	0.68215353709237	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	136b2 1088g2 2448f2 6800e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272a2

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	0	0	-2	-6	+	-4	-4	0	8	-4	6	-8	8	10	0	12	-8	-12	2	4	-16	10	-18

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Quadratic twists for elliptic curve 272a2

-4	8	-3	5	-7	-11	13	17	-19
136b2	1088g2	2448f2	6800e2	13328e2	32912o2	45968b2	4624a2	98192c2

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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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