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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 21312bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21312.bn3 | 21312bq1 | \([0, 0, 0, -120, 502]\) | \(4096000/37\) | \(1726272\) | \([]\) | \(2880\) | \(0.019349\) | \(\Gamma_0(N)\)-optimal |
| 21312.bn2 | 21312bq2 | \([0, 0, 0, -840, -9074]\) | \(1404928000/50653\) | \(2363266368\) | \([]\) | \(8640\) | \(0.56866\) | |
| 21312.bn1 | 21312bq3 | \([0, 0, 0, -67440, -6741002]\) | \(727057727488000/37\) | \(1726272\) | \([]\) | \(25920\) | \(1.1180\) |
Rank
sage: E.rank()
The elliptic curves in class 21312bq have rank \(1\).
Complex multiplication
The elliptic curves in class 21312bq do not have complex multiplication.Modular form 21312.2.a.bq
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
