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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 397800.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.dz1 | 397800dz2 | \([0, 0, 0, -1026795, -118080250]\) | \(641515943191354/338972315643\) | \(63260369434559232000\) | \([2]\) | \(10321920\) | \(2.4910\) | |
| 397800.dz2 | 397800dz1 | \([0, 0, 0, -589395, 172790750]\) | \(242664113947028/2205421101\) | \(205792253776512000\) | \([2]\) | \(5160960\) | \(2.1445\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 397800.dz do not have complex multiplication.Modular form 397800.2.a.dz
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.
