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	-342102016 = -1 · 212 · 174	Discriminant
Eigenvalues	2-  0 -2 -4  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11,890]	[a1,a2,a3,a4,a6]
Generators	[-1:30:1]	Generators of the group modulo torsion
j	-35937/83521	j-invariant
L	1.397785380624	L(r)(E,1)/r!
Ω	1.3728695590449	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	17a1 1088k4 2448o4 6800h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272b4

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 272b4

-4	8	-3	5	-7	-11	13	17	-19
17a1	1088k4	2448o4	6800h4	13328o4	32912t3	45968p3	4624e4	98192v3

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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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