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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 65025.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65025.u1 | 65025bo4 | \([1, -1, 1, -5896955, 5513226922]\) | \(82483294977/17\) | \(4674013947140625\) | \([2]\) | \(1179648\) | \(2.3940\) | |
| 65025.u2 | 65025bo2 | \([1, -1, 1, -369830, 85590172]\) | \(20346417/289\) | \(79458237101390625\) | \([2, 2]\) | \(589824\) | \(2.0474\) | |
| 65025.u3 | 65025bo1 | \([1, -1, 1, -44705, -1543328]\) | \(35937/17\) | \(4674013947140625\) | \([2]\) | \(294912\) | \(1.7008\) | \(\Gamma_0(N)\)-optimal |
| 65025.u4 | 65025bo3 | \([1, -1, 1, -44705, 230595922]\) | \(-35937/83521\) | \(-22963430522301890625\) | \([2]\) | \(1179648\) | \(2.3940\) |
Rank
sage: E.rank()
The elliptic curves in class 65025.u have rank \(0\).
Complex multiplication
The elliptic curves in class 65025.u do not have complex multiplication.Modular form 65025.2.a.u
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.
