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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 74529k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74529.ba2 | 74529k1 | \([0, 0, 1, -22607130, 43219369170]\) | \(-372736000/19683\) | \(-67476097852647492737547\) | \([]\) | \(5818176\) | \(3.1398\) | \(\Gamma_0(N)\)-optimal |
| 74529.ba1 | 74529k2 | \([0, 0, 1, -1853784660, 30721119647013]\) | \(-205514702848000/27\) | \(-92559805010490387843\) | \([3]\) | \(17454528\) | \(3.6891\) |
Rank
sage: E.rank()
The elliptic curves in class 74529k have rank \(0\).
Complex multiplication
The elliptic curves in class 74529k do not have complex multiplication.Modular form 74529.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
