Cremona's table of elliptic curves

50336 = 2⁵ · 11² · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	50336s	Isogeny class
Conductor	50336	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	22400	Modular degree for the optimal curve
Δ	-11791510016 = -1 · 29 · 116 · 13	Discriminant
Eigenvalues	2-  1  1 -3 11- 13+  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,5212]	[a1,a2,a3,a4,a6]
Generators	[57:1936:27]	Generators of the group modulo torsion
j	-8/13	j-invariant
L	6.3780685901204	L(r)(E,1)/r!
Ω	1.0237002204909	Real period
R	3.1152032901799	Regulator
r	1	Rank of the group of rational points
S	1.0000000000091	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50336d1 100672bq1 416a1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 50336s1

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
-	1	1	-3	-	+	3	-2	4	-2	4	5	12	-7	-9	4	6	4	-10	-15	2	8	4	2	10

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Quadratic twists for elliptic curve 50336s1

-4	8	-11
50336d1	100672bq1	416a1

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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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