Cremona's table of elliptic curves

272 = 2⁴ · 17

Field	Data	Notes
Atkin-Lehner	2- 17-	Signs for the Atkin-Lehner involutions
Class	272b	Isogeny class
Conductor	272	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1183744 = 212 · 172	Discriminant
Eigenvalues	2-  0 -2 -4  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-91,330]	[a1,a2,a3,a4,a6]
Generators	[-3:24:1]	Generators of the group modulo torsion
j	20346417/289	j-invariant
L	1.397785380624	L(r)(E,1)/r!
Ω	2.7457391180898	Real period
R	1.0181487173454	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17a2 1088k2 2448o2 6800h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272b2

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	-2	-4	0	-2	-	4	-4	6	-4	-2	-6	-4	0	6	12	-10	-4	4	-6	-12	4	10	2

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Quadratic twists for elliptic curve 272b2

-4	8	-3	5	-7	-11	13	17	-19
17a2	1088k2	2448o2	6800h2	13328o2	32912t2	45968p2	4624e2	98192v2

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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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