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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 163170fy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163170.s2 | 163170fy1 | \([1, -1, 0, -11288580, -14600090800]\) | \(-68700855708416547/24248320000\) | \(-56151477373501440000\) | \([2]\) | \(12165120\) | \(2.7595\) | \(\Gamma_0(N)\)-optimal |
| 163170.s1 | 163170fy2 | \([1, -1, 0, -180632580, -934375092400]\) | \(281470209323873024547/35046400\) | \(81156432141388800\) | \([2]\) | \(24330240\) | \(3.1060\) |
Rank
sage: E.rank()
The elliptic curves in class 163170fy have rank \(0\).
Complex multiplication
The elliptic curves in class 163170fy do not have complex multiplication.Modular form 163170.2.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.
