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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 38962.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38962.bb1 | 38962s2 | \([1, -1, 1, -610710, -180324559]\) | \(14219097381959625/285864951988\) | \(506427200208813268\) | \([2]\) | \(460800\) | \(2.1885\) | |
| 38962.bb2 | 38962s1 | \([1, -1, 1, 1550, -8401951]\) | \(232608375/17212788208\) | \(-30493504290552688\) | \([2]\) | \(230400\) | \(1.8419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38962.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 38962.bb do not have complex multiplication.Modular form 38962.2.a.bb
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.
