Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 27456.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27456.bw1 | 27456u2 | \([0, 1, 0, -833, 6687]\) | \(244140625/61347\) | \(16081747968\) | \([2]\) | \(16384\) | \(0.66836\) | |
| 27456.bw2 | 27456u1 | \([0, 1, 0, 127, 735]\) | \(857375/1287\) | \(-337379328\) | \([2]\) | \(8192\) | \(0.32178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27456.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 27456.bw do not have complex multiplication.Modular form 27456.2.a.bw
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.
