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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 38808.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.bi1 | 38808c2 | \([0, 0, 0, -33075, -2167074]\) | \(1687500/121\) | \(286922667322368\) | \([2]\) | \(138240\) | \(1.5210\) | |
| 38808.bi2 | 38808c1 | \([0, 0, 0, -6615, 166698]\) | \(54000/11\) | \(6520969711872\) | \([2]\) | \(69120\) | \(1.1744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38808.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.bi do not have complex multiplication.Modular form 38808.2.a.bi
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.
