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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 76440cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.cv1 | 76440cz1 | \([0, 1, 0, -963160, 170958080]\) | \(820221748268836/369468094905\) | \(44510773143017825280\) | \([2]\) | \(1806336\) | \(2.4655\) | \(\Gamma_0(N)\)-optimal |
| 76440.cv2 | 76440cz2 | \([0, 1, 0, 3342960, 1283659488]\) | \(17147425715207422/12872524043925\) | \(-3101572262387163801600\) | \([2]\) | \(3612672\) | \(2.8120\) |
Rank
sage: E.rank()
The elliptic curves in class 76440cz have rank \(1\).
Complex multiplication
The elliptic curves in class 76440cz do not have complex multiplication.Modular form 76440.2.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 Cremona 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 Cremona labels.
