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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 160446.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.z1 | 160446v1 | \([1, 1, 1, -365483, 77202137]\) | \(3047678972871625/304559880768\) | \(539546406933238848\) | \([2]\) | \(2580480\) | \(2.1388\) | \(\Gamma_0(N)\)-optimal |
| 160446.z2 | 160446v2 | \([1, 1, 1, 452477, 374612393]\) | \(5783051584712375/37533175779528\) | \(-66492310417156403208\) | \([2]\) | \(5160960\) | \(2.4854\) |
Rank
sage: E.rank()
The elliptic curves in class 160446.z have rank \(0\).
Complex multiplication
The elliptic curves in class 160446.z do not have complex multiplication.Modular form 160446.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
