Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 9408.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.cb1 | 9408da3 | \([0, 1, 0, -43969, 3534047]\) | \(2438569736/21\) | \(80957571072\) | \([2]\) | \(24576\) | \(1.2609\) | |
| 9408.cb2 | 9408da2 | \([0, 1, 0, -2809, 51911]\) | \(5088448/441\) | \(212513624064\) | \([2, 2]\) | \(12288\) | \(0.91432\) | |
| 9408.cb3 | 9408da1 | \([0, 1, 0, -604, -4978]\) | \(3241792/567\) | \(4269246912\) | \([2]\) | \(6144\) | \(0.56775\) | \(\Gamma_0(N)\)-optimal |
| 9408.cb4 | 9408da4 | \([0, 1, 0, 3071, 245951]\) | \(830584/7203\) | \(-27768446877696\) | \([2]\) | \(24576\) | \(1.2609\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.cb do not have complex multiplication.Modular form 9408.2.a.cb
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.
