Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 177744bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.u2 | 177744bw1 | \([0, -1, 0, -4408, 90557296]\) | \(-15625/5842368\) | \(-3542549056492142592\) | \([2]\) | \(2433024\) | \(2.2382\) | \(\Gamma_0(N)\)-optimal |
| 177744.u1 | 177744bw2 | \([0, -1, 0, -3051448, 2021161840]\) | \(5182207647625/91449288\) | \(55450733148147843072\) | \([2]\) | \(4866048\) | \(2.5847\) |
Rank
sage: E.rank()
The elliptic curves in class 177744bw have rank \(1\).
Complex multiplication
The elliptic curves in class 177744bw do not have complex multiplication.Modular form 177744.2.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.
