Properties

Label 145200fi
Number of curves $2$
Conductor $145200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 145200fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.bt2 145200fi1 \([0, -1, 0, -233933, 50699112]\) \(-3196715008/649539\) \(-287674490094750000\) \([2]\) \(1843200\) \(2.0725\) \(\Gamma_0(N)\)-optimal
145200.bt1 145200fi2 \([0, -1, 0, -3909308, 2976297612]\) \(932410994128/29403\) \(208356832332000000\) \([2]\) \(3686400\) \(2.4190\)  

Rank

sage: E.rank()
 

The elliptic curves in class 145200fi have rank \(1\).

Complex multiplication

The elliptic curves in class 145200fi do not have complex multiplication.

Modular form 145200.2.a.fi

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} + 6 q^{13} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.