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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 176400.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.dl1 | 176400jo1 | \([0, 0, 0, -903906675, -10437441036750]\) | \(551105805571803/1376829440\) | \(204051433560311070720000000\) | \([2]\) | \(92897280\) | \(3.9257\) | \(\Gamma_0(N)\)-optimal |
| 176400.dl2 | 176400jo2 | \([0, 0, 0, -565218675, -18353595660750]\) | \(-134745327251163/903920796800\) | \(-133964548587818287718400000000\) | \([2]\) | \(185794560\) | \(4.2723\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.dl do not have complex multiplication.Modular form 176400.2.a.dl
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.
