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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 424830eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.eb2 | 424830eb1 | \([1, 0, 1, 146372, -17252602]\) | \(41890384817/39795300\) | \(-329472697271615100\) | \([2]\) | \(5308416\) | \(2.0485\) | \(\Gamma_0(N)\)-optimal* |
424830.eb1 | 424830eb2 | \([1, 0, 1, -763978, -156354082]\) | \(5956317014383/2172381210\) | \(17985548463282722070\) | \([2]\) | \(10616832\) | \(2.3951\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830eb have rank \(0\).
Complex multiplication
The elliptic curves in class 424830eb do not have complex multiplication.Modular form 424830.2.a.eb
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.