Properties

Label 265200.fi
Number of curves $4$
Conductor $265200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 265200.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.fi1 265200fi3 \([0, 1, 0, -1562408, 751165188]\) \(26362547147244676/244298925\) \(3908782800000000\) \([2]\) \(3538944\) \(2.1555\)  
265200.fi2 265200fi2 \([0, 1, 0, -99908, 11140188]\) \(27572037674704/2472575625\) \(9890302500000000\) \([2, 2]\) \(1769472\) \(1.8089\)  
265200.fi3 265200fi1 \([0, 1, 0, -21783, -1047312]\) \(4572531595264/776953125\) \(194238281250000\) \([2]\) \(884736\) \(1.4623\) \(\Gamma_0(N)\)-optimal
265200.fi4 265200fi4 \([0, 1, 0, 112592, 52365188]\) \(9865576607324/79640206425\) \(-1274243302800000000\) \([2]\) \(3538944\) \(2.1555\)  

Rank

sage: E.rank()
 

The elliptic curves in class 265200.fi have rank \(0\).

Complex multiplication

The elliptic curves in class 265200.fi do not have complex multiplication.

Modular form 265200.2.a.fi

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4 q^{11} - q^{13} - q^{17} + 8 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.