Show commands:
SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 235950dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.dl2 | 235950dl1 | \([1, 0, 1, 491499, 217455148]\) | \(356400829/760500\) | \(-28019050296960937500\) | \([2]\) | \(5474304\) | \(2.4159\) | \(\Gamma_0(N)\)-optimal |
235950.dl1 | 235950dl2 | \([1, 0, 1, -3834251, 2354375648]\) | \(169204136291/32906250\) | \(1212362753233886718750\) | \([2]\) | \(10948608\) | \(2.7625\) |
Rank
sage: E.rank()
The elliptic curves in class 235950dl have rank \(1\).
Complex multiplication
The elliptic curves in class 235950dl do not have complex multiplication.Modular form 235950.2.a.dl
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.