Properties

Label 54208.i
Number of curves $2$
Conductor $54208$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 54208.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54208.i1 54208s2 \([0, 1, 0, -11031489, -9895057889]\) \(1278763167594532/375974556419\) \(43651030131946295066624\) \([2]\) \(3686400\) \(3.0500\)  
54208.i2 54208s1 \([0, 1, 0, 1852591, -1028234033]\) \(24226243449392/29774625727\) \(-864216116880176693248\) \([2]\) \(1843200\) \(2.7035\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54208.i have rank \(0\).

Complex multiplication

The elliptic curves in class 54208.i do not have complex multiplication.

Modular form 54208.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{5} - q^{7} + q^{9} + 4 q^{15} - 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.