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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5929.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5929.d1 | 5929b1 | \([0, -1, 1, -529657, 148545550]\) | \(-78843215872/539\) | \(-112339662867971\) | \([]\) | \(38400\) | \(1.8769\) | \(\Gamma_0(N)\)-optimal |
| 5929.d2 | 5929b2 | \([0, -1, 1, -292497, 281621955]\) | \(-13278380032/156590819\) | \(-32637031196065802891\) | \([]\) | \(115200\) | \(2.4262\) | |
| 5929.d3 | 5929b3 | \([0, -1, 1, 2612713, -7287902700]\) | \(9463555063808/115539436859\) | \(-24081004424295514300451\) | \([]\) | \(345600\) | \(2.9755\) |
Rank
sage: E.rank()
The elliptic curves in class 5929.d have rank \(1\).
Complex multiplication
The elliptic curves in class 5929.d do not have complex multiplication.Modular form 5929.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
