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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 44880.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.t1 | 44880bt4 | \([0, -1, 0, -43560, 3513840]\) | \(2231707882611241/7466910\) | \(30584463360\) | \([2]\) | \(98304\) | \(1.2337\) | |
| 44880.t2 | 44880bt3 | \([0, -1, 0, -8040, -207888]\) | \(14034143923561/3445241250\) | \(14111708160000\) | \([2]\) | \(98304\) | \(1.2337\) | |
| 44880.t3 | 44880bt2 | \([0, -1, 0, -2760, 54000]\) | \(567869252041/31472100\) | \(128909721600\) | \([2, 2]\) | \(49152\) | \(0.88716\) | |
| 44880.t4 | 44880bt1 | \([0, -1, 0, 120, 3312]\) | \(46268279/1211760\) | \(-4963368960\) | \([2]\) | \(24576\) | \(0.54058\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.t have rank \(1\).
Complex multiplication
The elliptic curves in class 44880.t do not have complex multiplication.Modular form 44880.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
