Cremona's table of elliptic curves

272 = 2⁴ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	272a	Isogeny class
Conductor	272	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	17408 = 210 · 17	Discriminant
Eigenvalues	2+ -2  0  0 -2 -6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,4]	[a1,a2,a3,a4,a6]
Generators	[-2:4:1]	Generators of the group modulo torsion
j	62500/17	j-invariant
L	1.2387792395146	L(r)(E,1)/r!
Ω	3.6319660374254	Real period
R	0.34107676854619	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	136b1 1088g1 2448f1 6800e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 272a1

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	0	0	-2	-6	+	-4	-4	0	8	-4	6	-8	8	10	0	12	-8	-12	2	4	-16	10	-18

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Quadratic twists for elliptic curve 272a1

-4	8	-3	5	-7	-11	13	17	-19
136b1	1088g1	2448f1	6800e1	13328e1	32912o1	45968b1	4624a1	98192c1

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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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