Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 58800.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.a1 | 58800gh2 | \([0, -1, 0, -2296408, -1338669968]\) | \(266916252066900625/162\) | \(812851200\) | \([]\) | \(622080\) | \(1.9324\) | |
| 58800.a2 | 58800gh1 | \([0, -1, 0, -28408, -1820048]\) | \(505318200625/4251528\) | \(21332466892800\) | \([]\) | \(207360\) | \(1.3831\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.a have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.a do not have complex multiplication.Modular form 58800.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
