Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 25200.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.co1 | 25200h1 | \([0, 0, 0, -6075, -87750]\) | \(78732/35\) | \(11022480000000\) | \([2]\) | \(55296\) | \(1.1982\) | \(\Gamma_0(N)\)-optimal |
| 25200.co2 | 25200h2 | \([0, 0, 0, 20925, -654750]\) | \(1608714/1225\) | \(-771573600000000\) | \([2]\) | \(110592\) | \(1.5447\) |
Rank
sage: E.rank()
The elliptic curves in class 25200.co have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.co do not have complex multiplication.Modular form 25200.2.a.co
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.
