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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 8880.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8880.k1 | 8880r2 | \([0, -1, 0, -3148885, 2151767197]\) | \(-843013059301831868416/61543395\) | \(-252081745920\) | \([]\) | \(90720\) | \(2.0848\) | |
| 8880.k2 | 8880r1 | \([0, -1, 0, -38485, 3025117]\) | \(-1539038632738816/66363694875\) | \(-271825694208000\) | \([]\) | \(30240\) | \(1.5355\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8880.k have rank \(0\).
Complex multiplication
The elliptic curves in class 8880.k do not have complex multiplication.Modular form 8880.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
