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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 177744.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.i1 | 177744bj2 | \([0, -1, 0, -109790952, -300148242576]\) | \(862551551257/269746176\) | \(45771337666162428953493504\) | \([]\) | \(40061952\) | \(3.6281\) | |
| 177744.i2 | 177744bj1 | \([0, -1, 0, -42629112, 107121155184]\) | \(50489872297/12096\) | \(2052485446206661853184\) | \([]\) | \(13353984\) | \(3.0788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177744.i have rank \(0\).
Complex multiplication
The elliptic curves in class 177744.i do not have complex multiplication.Modular form 177744.2.a.i
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.
