Properties

Label 238050.fi
Number of curves $2$
Conductor $238050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fi1")
 
E.isogeny_class()
 

Elliptic curves in class 238050.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
238050.fi1 238050fi2 \([1, -1, 1, -93556130, -241204828503]\) \(53706380371489/16171875000\) \(27269360055867919921875000\) \([2]\) \(48660480\) \(3.5859\)  
238050.fi2 238050fi1 \([1, -1, 1, 15946870, -25264912503]\) \(265971760991/317400000\) \(-535206640029834375000000\) \([2]\) \(24330240\) \(3.2393\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 238050.fi have rank \(0\).

Complex multiplication

The elliptic curves in class 238050.fi do not have complex multiplication.

Modular form 238050.2.a.fi

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + 2 q^{11} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.