Show commands:
SageMath
E = EllipticCurve("kl1")
E.isogeny_class()
Elliptic curves in class 187200kl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.ps2 | 187200kl1 | \([0, 0, 0, -5125260, 4465999600]\) | \(623295446073461/5458752\) | \(130397969055744000\) | \([2]\) | \(4718592\) | \(2.4510\) | \(\Gamma_0(N)\)-optimal |
187200.ps1 | 187200kl2 | \([0, 0, 0, -5240460, 4254722800]\) | \(666276475992821/58199166792\) | \(1390254246833946624000\) | \([2]\) | \(9437184\) | \(2.7975\) |
Rank
sage: E.rank()
The elliptic curves in class 187200kl have rank \(1\).
Complex multiplication
The elliptic curves in class 187200kl do not have complex multiplication.Modular form 187200.2.a.kl
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.