Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 331200x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331200.x1 | 331200x1 | \([0, 0, 0, -420, 3200]\) | \(592704/23\) | \(317952000\) | \([2]\) | \(122880\) | \(0.39892\) | \(\Gamma_0(N)\)-optimal |
331200.x2 | 331200x2 | \([0, 0, 0, 180, 11600]\) | \(5832/529\) | \(-58503168000\) | \([2]\) | \(245760\) | \(0.74549\) |
Rank
sage: E.rank()
The elliptic curves in class 331200x have rank \(2\).
Complex multiplication
The elliptic curves in class 331200x do not have complex multiplication.Modular form 331200.2.a.x
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.