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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 221760.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.eu1 | 221760eg2 | \([0, 0, 0, -18588, 973712]\) | \(59466754384/121275\) | \(1448500838400\) | \([2]\) | \(491520\) | \(1.2199\) | |
221760.eu2 | 221760eg1 | \([0, 0, 0, -768, 25688]\) | \(-67108864/343035\) | \(-256074255360\) | \([2]\) | \(245760\) | \(0.87338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221760.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.eu do not have complex multiplication.Modular form 221760.2.a.eu
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.