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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 91200fy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.dk2 | 91200fy1 | \([0, -1, 0, -2329633, 1375667137]\) | \(-341370886042369/1817528220\) | \(-7444595589120000000\) | \([2]\) | \(2580480\) | \(2.4659\) | \(\Gamma_0(N)\)-optimal |
| 91200.dk1 | 91200fy2 | \([0, -1, 0, -37321633, 87770915137]\) | \(1403607530712116449/39475350\) | \(161691033600000000\) | \([2]\) | \(5160960\) | \(2.8125\) |
Rank
sage: E.rank()
The elliptic curves in class 91200fy have rank \(1\).
Complex multiplication
The elliptic curves in class 91200fy do not have complex multiplication.Modular form 91200.2.a.fy
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.
