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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 105966x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 105966.k2 | 105966x1 | \([1, -1, 0, -16080498, 39321163476]\) | \(-1060490285861833/926330847232\) | \(-401681326162660503257088\) | \([2]\) | \(12902400\) | \(3.2264\) | \(\Gamma_0(N)\)-optimal |
| 105966.k1 | 105966x2 | \([1, -1, 0, -297041778, 1970030887380]\) | \(6684374974140996553/2097096248576\) | \(909355879420236406013184\) | \([2]\) | \(25804800\) | \(3.5730\) |
Rank
sage: E.rank()
The elliptic curves in class 105966x have rank \(1\).
Complex multiplication
The elliptic curves in class 105966x do not have complex multiplication.Modular form 105966.2.a.x
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.
