Cremona's table of elliptic curves

13356 = 2² · 3² · 7 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 53-	Signs for the Atkin-Lehner involutions
Class	13356g	Isogeny class
Conductor	13356	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-623137536 = -1 · 28 · 38 · 7 · 53	Discriminant
Eigenvalues	2- 3-  1 7- -3  0  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7752,262708]	[a1,a2,a3,a4,a6]
Generators	[53:27:1]	Generators of the group modulo torsion
j	-276056203264/3339	j-invariant
L	5.1673200456468	L(r)(E,1)/r!
Ω	1.4762618025884	Real period
R	0.8750683714411	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	53424bc1 4452d1 93492w1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13356g1

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	-	-3	0	0	7	-6	1	1	-7	5	4	-8	-	0	-9	2	2	-6	8	1	-8	10

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Quadratic twists for elliptic curve 13356g1

-4	-3	-7
53424bc1	4452d1	93492w1

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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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