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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 240448cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
240448.cb1 | 240448cb1 | \([0, -1, 0, -1100897, 444918497]\) | \(23320116793/2873\) | \(18178961765040128\) | \([2]\) | \(3538944\) | \(2.1433\) | \(\Gamma_0(N)\)-optimal |
240448.cb2 | 240448cb2 | \([0, -1, 0, -1008417, 522657185]\) | \(-17923019113/8254129\) | \(-52228157150960287744\) | \([2]\) | \(7077888\) | \(2.4899\) |
Rank
sage: E.rank()
The elliptic curves in class 240448cb have rank \(2\).
Complex multiplication
The elliptic curves in class 240448cb do not have complex multiplication.Modular form 240448.2.a.cb
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.