Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 350658bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.bb2 | 350658bb1 | \([1, -1, 0, -20822247, -52961705307]\) | \(-52802213121625/33540304392\) | \(-634192905755062988594568\) | \([]\) | \(52918272\) | \(3.2687\) | \(\Gamma_0(N)\)-optimal |
| 350658.bb1 | 350658bb2 | \([1, -1, 0, -1888647822, -31591345965228]\) | \(-39402364010111991625/3532128768\) | \(-66786841905145782723072\) | \([]\) | \(158754816\) | \(3.8180\) |
Rank
sage: E.rank()
The elliptic curves in class 350658bb have rank \(0\).
Complex multiplication
The elliptic curves in class 350658bb do not have complex multiplication.Modular form 350658.2.a.bb
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.
