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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 13923b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13923.e1 | 13923b1 | \([1, -1, 1, -421283, -105127766]\) | \(420100556152674123/62939003491\) | \(1238828405713353\) | \([2]\) | \(138240\) | \(1.9093\) | \(\Gamma_0(N)\)-optimal |
| 13923.e2 | 13923b2 | \([1, -1, 1, -382268, -125415566]\) | \(-313859434290315003/164114213839849\) | \(-3230260071009747867\) | \([2]\) | \(276480\) | \(2.2559\) |
Rank
sage: E.rank()
The elliptic curves in class 13923b have rank \(0\).
Complex multiplication
The elliptic curves in class 13923b do not have complex multiplication.Modular form 13923.2.a.b
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.
