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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 58800jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.fk2 | 58800jb1 | \([0, 1, 0, -408, 7188]\) | \(-2401/6\) | \(-18816000000\) | \([]\) | \(40320\) | \(0.65939\) | \(\Gamma_0(N)\)-optimal |
| 58800.fk1 | 58800jb2 | \([0, 1, 0, -56408, -5368812]\) | \(-6329617441/279936\) | \(-877879296000000\) | \([]\) | \(282240\) | \(1.6323\) |
Rank
sage: E.rank()
The elliptic curves in class 58800jb have rank \(0\).
Complex multiplication
The elliptic curves in class 58800jb do not have complex multiplication.Modular form 58800.2.a.jb
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
