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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 101430.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.dz1 | 101430cz1 | \([1, -1, 1, -241403483, 603658895627]\) | \(489781415227546051766883/233890092903563264000\) | \(742957259580305490051072000\) | \([2]\) | \(49545216\) | \(3.8499\) | \(\Gamma_0(N)\)-optimal |
| 101430.dz2 | 101430cz2 | \([1, -1, 1, 866482597, 4590719320331]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-50740221307716661883904000000\) | \([2]\) | \(99090432\) | \(4.1965\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.dz have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.dz do not have complex multiplication.Modular form 101430.2.a.dz
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.
