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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 490245be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490245.be2 | 490245be1 | \([0, -1, 1, -6077045, -5135926237]\) | \(210966209738334797824/25153051046653125\) | \(2959231302587693503125\) | \([]\) | \(24494400\) | \(2.8509\) | \(\Gamma_0(N)\)-optimal* |
490245.be1 | 490245be2 | \([0, -1, 1, -116574005, 483754765556]\) | \(1489157481162281146384384/2616603057861328125\) | \(307840733154327392578125\) | \([]\) | \(73483200\) | \(3.4002\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 490245be have rank \(0\).
Complex multiplication
The elliptic curves in class 490245be do not have complex multiplication.Modular form 490245.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.