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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 217672.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217672.q1 | 217672t2 | \([0, -1, 0, -451624, 110706348]\) | \(1030541881826/62236321\) | \(615225004707203072\) | \([2]\) | \(2073600\) | \(2.1658\) | |
217672.q2 | 217672t1 | \([0, -1, 0, -444864, 114354044]\) | \(1969910093092/7889\) | \(38992584909824\) | \([2]\) | \(1036800\) | \(1.8193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 217672.q have rank \(0\).
Complex multiplication
The elliptic curves in class 217672.q do not have complex multiplication.Modular form 217672.2.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 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.