Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 177744bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.h2 | 177744bi1 | \([0, -1, 0, -337, -1616]\) | \(501563392/137781\) | \(1166178384\) | \([]\) | \(103680\) | \(0.44735\) | \(\Gamma_0(N)\)-optimal |
| 177744.h1 | 177744bi2 | \([0, -1, 0, -25177, -1529276]\) | \(208534179069952/9261\) | \(78385104\) | \([]\) | \(311040\) | \(0.99666\) |
Rank
sage: E.rank()
The elliptic curves in class 177744bi have rank \(0\).
Complex multiplication
The elliptic curves in class 177744bi do not have complex multiplication.Modular form 177744.2.a.bi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
