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	4	Product of Tamagawa factors cp
Δ	69632 = 212 · 17	Discriminant
Eigenvalues	2-  0 -2 -4  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1451,21274]	[a1,a2,a3,a4,a6]
Generators	[-3:160:1]	Generators of the group modulo torsion
j	82483294977/17	j-invariant
L	1.397785380624	L(r)(E,1)/r!
Ω	2.7457391180898	Real period
R	2.0362974346907	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	17a3 1088k3 2448o3 6800h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272b3

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 272b3

-4	8	-3	5	-7	-11	13	17	-19
17a3	1088k3	2448o3	6800h3	13328o3	32912t4	45968p4	4624e3	98192v4

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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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