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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 217800gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217800.fb1 | 217800gb1 | \([0, 0, 0, -226875, 12311750]\) | \(62500/33\) | \(681895087632000000\) | \([2]\) | \(2211840\) | \(2.1135\) | \(\Gamma_0(N)\)-optimal |
| 217800.fb2 | 217800gb2 | \([0, 0, 0, 862125, 96164750]\) | \(1714750/1089\) | \(-45005075783712000000\) | \([2]\) | \(4423680\) | \(2.4601\) |
Rank
sage: E.rank()
The elliptic curves in class 217800gb have rank \(1\).
Complex multiplication
The elliptic curves in class 217800gb do not have complex multiplication.Modular form 217800.2.a.gb
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.
