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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 44880cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.bk1 | 44880cf1 | \([0, 1, 0, -1416, 16884]\) | \(76711450249/12622500\) | \(51701760000\) | \([2]\) | \(46080\) | \(0.77732\) | \(\Gamma_0(N)\)-optimal |
| 44880.bk2 | 44880cf2 | \([0, 1, 0, 2584, 98484]\) | \(465664585751/1274620050\) | \(-5220843724800\) | \([2]\) | \(92160\) | \(1.1239\) |
Rank
sage: E.rank()
The elliptic curves in class 44880cf have rank \(2\).
Complex multiplication
The elliptic curves in class 44880cf do not have complex multiplication.Modular form 44880.2.a.cf
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.
