Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 398502bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 398502.bq2 | 398502bq1 | \([1, -1, 1, -3247367, -2140065313]\) | \(1076291879750641/60150618144\) | \(211654612314493399584\) | \([]\) | \(14515200\) | \(2.6551\) | \(\Gamma_0(N)\)-optimal |
| 398502.bq1 | 398502bq2 | \([1, -1, 1, -345335477, 2470156577867]\) | \(1294373635812597347281/2083292441154\) | \(7330572279649097140194\) | \([]\) | \(72576000\) | \(3.4599\) |
Rank
sage: E.rank()
The elliptic curves in class 398502bq have rank \(1\).
Complex multiplication
The elliptic curves in class 398502bq do not have complex multiplication.Modular form 398502.2.a.bq
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
