Cremona's table of elliptic curves

506 = 2 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2+ 11+ 23+	Signs for the Atkin-Lehner involutions
Class	506a	Isogeny class
Conductor	506	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	32384 = 27 · 11 · 23	Discriminant
Eigenvalues	2+ -2  1 -1 11+  3  3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-48,-130]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1]	Generators of the group modulo torsion
j	11867954041/32384	j-invariant
L	1.2018688781118	L(r)(E,1)/r!
Ω	1.8186526895687	Real period
R	0.66085673477152	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4048l1 16192h1 4554bi1 12650s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 506a1

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	1	-1	+	3	3	-6	+	-1	-7	-5	-2	-8	-1	-6	-10	-8	7	-5	4	11	12	6	2

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Quadratic twists for elliptic curve 506a1

-4	8	-3	5	-7	-11	13	-23
4048l1	16192h1	4554bi1	12650s1	24794b1	5566e1	85514o1	11638l1

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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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