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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 124950.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.fi1 | 124950fs2 | \([1, 1, 1, -467363, -123155719]\) | \(6141556990297/1019592\) | \(1874280925125000\) | \([2]\) | \(1179648\) | \(1.9386\) | |
124950.fi2 | 124950fs1 | \([1, 1, 1, -26363, -2321719]\) | \(-1102302937/616896\) | \(-1134018711000000\) | \([2]\) | \(589824\) | \(1.5920\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.fi have rank \(0\).
Complex multiplication
The elliptic curves in class 124950.fi do not have complex multiplication.Modular form 124950.2.a.fi
sage: E.q_eigenform(10)
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.