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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 141960.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141960.v1 | 141960by1 | \([0, -1, 0, -3321920, -1095977988]\) | \(820221748268836/369468094905\) | \(1826152371917115540480\) | \([2]\) | \(6322176\) | \(2.7750\) | \(\Gamma_0(N)\)-optimal |
| 141960.v2 | 141960by2 | \([0, -1, 0, 11529800, -8218862900]\) | \(17147425715207422/12872524043925\) | \(-127248824131447982745600\) | \([2]\) | \(12644352\) | \(3.1216\) |
Rank
sage: E.rank()
The elliptic curves in class 141960.v have rank \(0\).
Complex multiplication
The elliptic curves in class 141960.v do not have complex multiplication.Modular form 141960.2.a.v
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.
