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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 13520.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.bc1 | 13520bb3 | \([0, -1, 0, -6985, 226992]\) | \(488095744/125\) | \(9653618000\) | \([2]\) | \(13824\) | \(0.90183\) | |
| 13520.bc2 | 13520bb4 | \([0, -1, 0, -6140, 283100]\) | \(-20720464/15625\) | \(-19307236000000\) | \([2]\) | \(27648\) | \(1.2484\) | |
| 13520.bc3 | 13520bb1 | \([0, -1, 0, -225, -820]\) | \(16384/5\) | \(386144720\) | \([2]\) | \(4608\) | \(0.35252\) | \(\Gamma_0(N)\)-optimal |
| 13520.bc4 | 13520bb2 | \([0, -1, 0, 620, -6228]\) | \(21296/25\) | \(-30891577600\) | \([2]\) | \(9216\) | \(0.69910\) |
Rank
sage: E.rank()
The elliptic curves in class 13520.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 13520.bc do not have complex multiplication.Modular form 13520.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
