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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 105963n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 105963.k2 | 105963n1 | \([0, 1, 1, -61403, -6333934]\) | \(-5304438784000/497763387\) | \(-2402608796242083\) | \([]\) | \(421200\) | \(1.6933\) | \(\Gamma_0(N)\)-optimal |
| 105963.k1 | 105963n2 | \([0, 1, 1, -5080703, -4409615245]\) | \(-3004935183806464000/2037123\) | \(-9832803630507\) | \([]\) | \(1263600\) | \(2.2426\) |
Rank
sage: E.rank()
The elliptic curves in class 105963n have rank \(0\).
Complex multiplication
The elliptic curves in class 105963n do not have complex multiplication.Modular form 105963.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
