Cremona's table of elliptic curves

272 = 2⁴ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17-	Signs for the Atkin-Lehner involutions
Class	272c	Isogeny class
Conductor	272	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-295936 = -1 · 210 · 172	Discriminant
Eigenvalues	2+  2 -2  2  6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,16,-16]	[a1,a2,a3,a4,a6]
j	415292/289	j-invariant
L	1.7365317314057	L(r)(E,1)/r!
Ω	1.7365317314057	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	136a2 1088m2 2448c2 6800d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272c2

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	-2	2	6	2	-	0	-6	-10	-2	6	-6	8	0	-10	8	14	-4	-2	-14	10	-8	-10	2

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Quadratic twists for elliptic curve 272c2

-4	8	-3	5	-7	-11	13	17	-19
136a2	1088m2	2448c2	6800d2	13328d2	32912f2	45968f2	4624d2	98192e2

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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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