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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 24255.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.o1 | 24255bu4 | \([1, -1, 1, -9129812, -3005996164]\) | \(981281029968144361/522287841796875\) | \(44794602236379638671875\) | \([2]\) | \(1769472\) | \(3.0377\) | |
| 24255.o2 | 24255bu2 | \([1, -1, 1, -7165157, -7372245436]\) | \(474334834335054841/607815140625\) | \(52129946896475765625\) | \([2, 2]\) | \(884736\) | \(2.6912\) | |
| 24255.o3 | 24255bu1 | \([1, -1, 1, -7162952, -7377016174]\) | \(473897054735271721/779625\) | \(66865412084625\) | \([2]\) | \(442368\) | \(2.3446\) | \(\Gamma_0(N)\)-optimal |
| 24255.o4 | 24255bu3 | \([1, -1, 1, -5235782, -11433193936]\) | \(-185077034913624841/551466161890875\) | \(-47297113568138374045875\) | \([2]\) | \(1769472\) | \(3.0377\) |
Rank
sage: E.rank()
The elliptic curves in class 24255.o have rank \(1\).
Complex multiplication
The elliptic curves in class 24255.o do not have complex multiplication.Modular form 24255.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
