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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 14896bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14896.x2 | 14896bd1 | \([0, 1, 0, -12168, 512756]\) | \(-413493625/152\) | \(-73247326208\) | \([]\) | \(18144\) | \(1.0527\) | \(\Gamma_0(N)\)-optimal |
| 14896.x3 | 14896bd2 | \([0, 1, 0, 7432, 1966292]\) | \(94196375/3511808\) | \(-1692306224709632\) | \([]\) | \(54432\) | \(1.6020\) | |
| 14896.x1 | 14896bd3 | \([0, 1, 0, -67048, -53774540]\) | \(-69173457625/2550136832\) | \(-1228886213214076928\) | \([]\) | \(163296\) | \(2.1513\) |
Rank
sage: E.rank()
The elliptic curves in class 14896bd have rank \(0\).
Complex multiplication
The elliptic curves in class 14896bd do not have complex multiplication.Modular form 14896.2.a.bd
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.
