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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 486720.ib
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.ib1 | 486720ib2 | \([0, 0, 0, -20748, -938288]\) | \(18821096/3645\) | \(191295631687680\) | \([2]\) | \(2064384\) | \(1.4574\) | \(\Gamma_0(N)\)-optimal* |
486720.ib2 | 486720ib1 | \([0, 0, 0, 2652, -86528]\) | \(314432/675\) | \(-4428139622400\) | \([2]\) | \(1032192\) | \(1.1108\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720.ib have rank \(0\).
Complex multiplication
The elliptic curves in class 486720.ib do not have complex multiplication.Modular form 486720.2.a.ib
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 LMFDB 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 LMFDB labels.