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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 443760q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.q2 | 443760q1 | \([0, -1, 0, -10936, -11798864]\) | \(-444194947/184528125\) | \(-60093553190400000\) | \([2]\) | \(5350400\) | \(1.8987\) | \(\Gamma_0(N)\)-optimal* |
443760.q1 | 443760q2 | \([0, -1, 0, -846856, -296680400]\) | \(206246988924787/2373046875\) | \(772808040000000000\) | \([2]\) | \(10700800\) | \(2.2453\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760q have rank \(0\).
Complex multiplication
The elliptic curves in class 443760q do not have complex multiplication.Modular form 443760.2.a.q
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.