Cremona's table of elliptic curves

544 = 2⁵ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	544a	Isogeny class
Conductor	544	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	1088 = 26 · 17	Discriminant
Eigenvalues	2+  0  0 -2 -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	216000/17	j-invariant
L	1.9135747396752	L(r)(E,1)/r!
Ω	4.794196062329	Real period
R	0.79828806114601	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	544d1 1088b1 4896q1 13600s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 544a1

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

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Quadratic twists for elliptic curve 544a1

-4	8	-3	5	-7	-11	13	17
544d1	1088b1	4896q1	13600s1	26656d1	65824m1	91936l1	9248a1

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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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