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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 26026.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26026.m1 | 26026q2 | \([1, -1, 1, -3145291, -2140796069]\) | \(712928482228623753/2093213298176\) | \(10103540786555600384\) | \([2]\) | \(725760\) | \(2.5168\) | |
| 26026.m2 | 26026q1 | \([1, -1, 1, -116811, -60836005]\) | \(-36518366116233/310426468352\) | \(-1498369271279648768\) | \([2]\) | \(362880\) | \(2.1702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26026.m have rank \(0\).
Complex multiplication
The elliptic curves in class 26026.m do not have complex multiplication.Modular form 26026.2.a.m
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.
