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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 141120.cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.cz1 | 141120lq1 | \([0, 0, 0, -997248, 383301128]\) | \(1248870793216/42525\) | \(3734737198617600\) | \([2]\) | \(1474560\) | \(2.0797\) | \(\Gamma_0(N)\)-optimal |
| 141120.cz2 | 141120lq2 | \([0, 0, 0, -953148, 418739888]\) | \(-68150496976/14467005\) | \(-20328921519515320320\) | \([2]\) | \(2949120\) | \(2.4263\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.cz have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.cz do not have complex multiplication.Modular form 141120.2.a.cz
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.
