Properties

Label 55488u
Number of curves $2$
Conductor $55488$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 55488u have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 - 5 T + 13 T^{2}\) 1.13.af
\(19\) \( 1 + 7 T + 19 T^{2}\) 1.19.h
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 55488u do not have complex multiplication.

Modular form 55488.2.a.u

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} - 4 q^{7} + q^{9} - 3 q^{11} - 2 q^{13} - 3 q^{15} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 55488u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55488.bz2 55488u1 \([0, -1, 0, -29667969, -62530585983]\) \(-1579268174113/10077696\) \(-18428608606407474806784\) \([]\) \(7402752\) \(3.1096\) \(\Gamma_0(N)\)-optimal
55488.bz1 55488u2 \([0, -1, 0, -2406773889, -45445761389439]\) \(-843137281012581793/216\) \(-394989039060516864\) \([]\) \(22208256\) \(3.6589\)