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	506f	Isogeny class
Conductor	506	Conductor
∏ cp	13	Product of Tamagawa factors cp
deg	104	Modular degree for the optimal curve
Δ	2072576 = 213 · 11 · 23	Discriminant
Eigenvalues	2- -2 -1 -1 11- -3 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-86,292]	[a1,a2,a3,a4,a6]
Generators	[4:2:1]	Generators of the group modulo torsion
j	70393838689/2072576	j-invariant
L	2.0097923472732	L(r)(E,1)/r!
Ω	2.6021500295055	Real period
R	0.059412182070875	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	4048f1 16192b1 4554h1 12650n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 506f1

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	-5	-6	+	-7	1	5	-6	8	-1	14	6	-8	-7	3	8	-5	12	-14	-10

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Quadratic twists for elliptic curve 506f1

-4	8	-3	5	-7	-11	13	-23
4048f1	16192b1	4554h1	12650n1	24794bq1	5566b1	85514c1	11638q1

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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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