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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 177744bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.y2 | 177744bs1 | \([0, -1, 0, 8472, 1311408]\) | \(1349232625/15752961\) | \(-785065068490752\) | \([2]\) | \(540672\) | \(1.5390\) | \(\Gamma_0(N)\)-optimal |
| 177744.y1 | 177744bs2 | \([0, -1, 0, -140568, 18957744]\) | \(6163717745375/466948881\) | \(23270879375880192\) | \([2]\) | \(1081344\) | \(1.8856\) |
Rank
sage: E.rank()
The elliptic curves in class 177744bs have rank \(2\).
Complex multiplication
The elliptic curves in class 177744bs do not have complex multiplication.Modular form 177744.2.a.bs
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.
