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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 139230be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139230.dh2 | 139230be1 | \([1, -1, 1, 1732, 155391]\) | \(788632918919/14845259520\) | \(-10822194190080\) | \([2]\) | \(344064\) | \(1.1815\) | \(\Gamma_0(N)\)-optimal |
| 139230.dh1 | 139230be2 | \([1, -1, 1, -34988, 2387967]\) | \(6497434355239801/405606692400\) | \(295687278759600\) | \([2]\) | \(688128\) | \(1.5280\) |
Rank
sage: E.rank()
The elliptic curves in class 139230be have rank \(1\).
Complex multiplication
The elliptic curves in class 139230be do not have complex multiplication.Modular form 139230.2.a.be
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.
