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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 44100.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.q1 | 44100ce2 | \([0, 0, 0, -8878800, -10183155500]\) | \(-225637236736/1715\) | \(-588355590060000000\) | \([]\) | \(1244160\) | \(2.5845\) | |
44100.q2 | 44100ce1 | \([0, 0, 0, -58800, -26925500]\) | \(-65536/875\) | \(-300181423500000000\) | \([]\) | \(414720\) | \(2.0352\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44100.q have rank \(0\).
Complex multiplication
The elliptic curves in class 44100.q do not have complex multiplication.Modular form 44100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.