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
deg	16	Modular degree for the optimal curve
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,-11,-6]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	35937/17	j-invariant
L	1.397785380624	L(r)(E,1)/r!
Ω	2.7457391180898	Real period
R	0.50907435867268	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	17a4 1088k1 2448o1 6800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272b1

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 272b1

-4	8	-3	5	-7	-11	13	17	-19
17a4	1088k1	2448o1	6800h1	13328o1	32912t1	45968p1	4624e1	98192v1

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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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