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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 180336bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.bq1 | 180336bx1 | \([0, -1, 0, -2996176, 1996999168]\) | \(147815204204011553/15178486401\) | \(305446517506510848\) | \([2]\) | \(5111808\) | \(2.3879\) | \(\Gamma_0(N)\)-optimal |
| 180336.bq2 | 180336bx2 | \([0, -1, 0, -2766336, 2316017088]\) | \(-116340772335201233/47730591665289\) | \(-960513625504009654272\) | \([2]\) | \(10223616\) | \(2.7345\) |
Rank
sage: E.rank()
The elliptic curves in class 180336bx have rank \(0\).
Complex multiplication
The elliptic curves in class 180336bx do not have complex multiplication.Modular form 180336.2.a.bx
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.
