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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 38646.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38646.z1 | 38646bb2 | \([1, -1, 1, -22761500, 22467287135]\) | \(1788952473315990499029625/736296634487918297088\) | \(536760246541692438577152\) | \([3]\) | \(4872960\) | \(3.2508\) | |
| 38646.z2 | 38646bb1 | \([1, -1, 1, -10542245, -13171144867]\) | \(177744208950637895247625/17681950027579392\) | \(12890141570105376768\) | \([]\) | \(1624320\) | \(2.7015\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38646.z have rank \(0\).
Complex multiplication
The elliptic curves in class 38646.z do not have complex multiplication.Modular form 38646.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
