Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 54080bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.r2 | 54080bw1 | \([0, 1, 0, -4385, -44225]\) | \(16194277/8000\) | \(4607442944000\) | \([2]\) | \(82944\) | \(1.1230\) | \(\Gamma_0(N)\)-optimal |
| 54080.r1 | 54080bw2 | \([0, 1, 0, -37665, 2771263]\) | \(10260751717/125000\) | \(71991296000000\) | \([2]\) | \(165888\) | \(1.4696\) |
Rank
sage: E.rank()
The elliptic curves in class 54080bw have rank \(1\).
Complex multiplication
The elliptic curves in class 54080bw do not have complex multiplication.Modular form 54080.2.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 Cremona 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 Cremona labels.
