Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 18032.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18032.v1 | 18032ba2 | \([0, -1, 0, -474728, 118023536]\) | \(24553362849625/1755162752\) | \(845795912130756608\) | \([2]\) | \(258048\) | \(2.1869\) | |
| 18032.v2 | 18032ba1 | \([0, -1, 0, 27032, 8037744]\) | \(4533086375/60669952\) | \(-29236261612945408\) | \([2]\) | \(129024\) | \(1.8403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18032.v have rank \(0\).
Complex multiplication
The elliptic curves in class 18032.v do not have complex multiplication.Modular form 18032.2.a.v
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.
