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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 72450.cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.cz1 | 72450et1 | \([1, -1, 1, -884930, -27402303]\) | \(53826041237093/30917811456\) | \(44021649514500000000\) | \([2]\) | \(1720320\) | \(2.4589\) | \(\Gamma_0(N)\)-optimal |
| 72450.cz2 | 72450et2 | \([1, -1, 1, 3525070, -221442303]\) | \(3402275649500827/1983669431184\) | \(-2824404326822531250000\) | \([2]\) | \(3440640\) | \(2.8055\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 72450.cz do not have complex multiplication.Modular form 72450.2.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.
