Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 9408.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.bc1 | 9408ca3 | \([0, -1, 0, -29857, 1993153]\) | \(381775972/567\) | \(4371708837888\) | \([2]\) | \(24576\) | \(1.3265\) | |
| 9408.bc2 | 9408ca2 | \([0, -1, 0, -2417, 11985]\) | \(810448/441\) | \(850054496256\) | \([2, 2]\) | \(12288\) | \(0.97991\) | |
| 9408.bc3 | 9408ca1 | \([0, -1, 0, -1437, -20355]\) | \(2725888/21\) | \(2529924096\) | \([2]\) | \(6144\) | \(0.63334\) | \(\Gamma_0(N)\)-optimal |
| 9408.bc4 | 9408ca4 | \([0, -1, 0, 9343, 84897]\) | \(11696828/7203\) | \(-55536893755392\) | \([2]\) | \(24576\) | \(1.3265\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.bc do not have complex multiplication.Modular form 9408.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
