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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 222768.gd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222768.gd1 | 222768dn1 | \([0, 0, 0, -6740523, 6734917530]\) | \(420100556152674123/62939003491\) | \(5074241149801893888\) | \([2]\) | \(8847360\) | \(2.6025\) | \(\Gamma_0(N)\)-optimal |
| 222768.gd2 | 222768dn2 | \([0, 0, 0, -6116283, 8032712490]\) | \(-313859434290315003/164114213839849\) | \(-13231145250855927263232\) | \([2]\) | \(17694720\) | \(2.9491\) |
Rank
sage: E.rank()
The elliptic curves in class 222768.gd have rank \(0\).
Complex multiplication
The elliptic curves in class 222768.gd do not have complex multiplication.Modular form 222768.2.a.gd
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.
