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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 331200v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331200.v1 | 331200v1 | \([0, 0, 0, -94500, 10800000]\) | \(592704/23\) | \(3621672000000000\) | \([2]\) | \(1843200\) | \(1.7529\) | \(\Gamma_0(N)\)-optimal |
331200.v2 | 331200v2 | \([0, 0, 0, 40500, 39150000]\) | \(5832/529\) | \(-666387648000000000\) | \([2]\) | \(3686400\) | \(2.0995\) |
Rank
sage: E.rank()
The elliptic curves in class 331200v have rank \(1\).
Complex multiplication
The elliptic curves in class 331200v do not have complex multiplication.Modular form 331200.2.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 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.