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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 104880.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104880.k1 | 104880bg2 | \([0, -1, 0, -549755797136, -156892554008614464]\) | \(4486144075680775880097697589357030929/16270828779444633600\) | \(66645314680605219225600\) | \([2]\) | \(333312000\) | \(4.9606\) | |
| 104880.k2 | 104880bg1 | \([0, -1, 0, -34359721616, -2451439919453760]\) | \(-1095248516670909925403006195052049/2085842527704615412039680\) | \(-8543610993478104727714529280\) | \([2]\) | \(166656000\) | \(4.6141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 104880.k have rank \(1\).
Complex multiplication
The elliptic curves in class 104880.k do not have complex multiplication.Modular form 104880.2.a.k
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.
