Cremona's table of elliptic curves

53361 = 3² · 7² · 11²

Field	Data	Notes
Atkin-Lehner	3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	53361bm	Isogeny class
Conductor	53361	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	-1255701777561 = -1 · 36 · 76 · 114	Discriminant
Eigenvalues	-1 3-  1 7- 11- -1 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1112,-55492]	[a1,a2,a3,a4,a6]
Generators	[48:-20:1] [58:240:1]	Generators of the group modulo torsion
j	-121	j-invariant
L	6.7497944002395	L(r)(E,1)/r!
Ω	0.36358524797052	Real period
R	1.5470453485844	Regulator
r	2	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5929d1 1089h1 53361bh2	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 53361bm1

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	-	-	-1	-5	-6	-2	-9	2	-3	-5	0	2	-9	8	-6	2	-12	2	-10	6	-9	13

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Quadratic twists for elliptic curve 53361bm1

-3	-7	-11
5929d1	1089h1	53361bh2

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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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