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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 107712dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.bl2 | 107712dz1 | \([0, 0, 0, -314796, 66518224]\) | \(18052771191337/444958272\) | \(85032849975017472\) | \([2]\) | \(1032192\) | \(2.0322\) | \(\Gamma_0(N)\)-optimal |
| 107712.bl1 | 107712dz2 | \([0, 0, 0, -706476, -131985200]\) | \(204055591784617/78708537864\) | \(15041435822419083264\) | \([2]\) | \(2064384\) | \(2.3788\) |
Rank
sage: E.rank()
The elliptic curves in class 107712dz have rank \(0\).
Complex multiplication
The elliptic curves in class 107712dz do not have complex multiplication.Modular form 107712.2.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 Cremona 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 Cremona labels.
