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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 422370.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 422370.z1 | 422370z1 | \([1, -1, 0, -3831180, 2169169360]\) | \(713797912953/179978240\) | \(1568072625729740881920\) | \([2]\) | \(20428800\) | \(2.7769\) | \(\Gamma_0(N)\)-optimal |
| 422370.z2 | 422370z2 | \([1, -1, 0, 9338100, 13813446736]\) | \(10336013655687/15445788800\) | \(-134572482762821903030400\) | \([2]\) | \(40857600\) | \(3.1234\) |
Rank
sage: E.rank()
The elliptic curves in class 422370.z have rank \(0\).
Complex multiplication
The elliptic curves in class 422370.z do not have complex multiplication.Modular form 422370.2.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.
