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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 134064.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134064.co1 | 134064bg3 | \([0, 0, 0, -603435, 1451309146]\) | \(-69173457625/2550136832\) | \(-895858049433062080512\) | \([]\) | \(4898880\) | \(2.7006\) | |
| 134064.co2 | 134064bg1 | \([0, 0, 0, -109515, -13953926]\) | \(-413493625/152\) | \(-53397300805632\) | \([]\) | \(544320\) | \(1.6020\) | \(\Gamma_0(N)\)-optimal |
| 134064.co3 | 134064bg2 | \([0, 0, 0, 66885, -53022998]\) | \(94196375/3511808\) | \(-1233691237813321728\) | \([]\) | \(1632960\) | \(2.1513\) |
Rank
sage: E.rank()
The elliptic curves in class 134064.co have rank \(1\).
Complex multiplication
The elliptic curves in class 134064.co do not have complex multiplication.Modular form 134064.2.a.co
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
