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	506d	Isogeny class
Conductor	506	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	118533536 = 25 · 115 · 23	Discriminant
Eigenvalues	2+  0 -1  1 11- -7  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-935,11229]	[a1,a2,a3,a4,a6]
Generators	[17:-3:1]	Generators of the group modulo torsion
j	90452336967369/118533536	j-invariant
L	1.456780907573	L(r)(E,1)/r!
Ω	1.8611497781033	Real period
R	0.15654633761476	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	4048c1 16192d1 4554w1 12650t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 506d1

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	-1	1	-	-7	3	-2	-	-3	-5	1	-4	-10	5	6	-8	2	-5	5	-4	-7	-6	4	16

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Quadratic twists for elliptic curve 506d1

-4	8	-3	5	-7	-11	13	-23
4048c1	16192d1	4554w1	12650t1	24794t1	5566g1	85514k1	11638a1

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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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