Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 34272.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34272.g1 | 34272be2 | \([0, 0, 0, -52491, 104974]\) | \(42852953779784/24786408969\) | \(9251477574861312\) | \([2]\) | \(184320\) | \(1.7531\) | |
| 34272.g2 | 34272be1 | \([0, 0, 0, 13119, 13120]\) | \(5352028359488/3098832471\) | \(-144579127766976\) | \([2]\) | \(92160\) | \(1.4065\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34272.g have rank \(1\).
Complex multiplication
The elliptic curves in class 34272.g do not have complex multiplication.Modular form 34272.2.a.g
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 LMFDB 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 LMFDB labels.
