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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 180336.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.cy1 | 180336v1 | \([0, 1, 0, -361057, -83623702]\) | \(13478411517952/304317\) | \(117527561365968\) | \([2]\) | \(1105920\) | \(1.8139\) | \(\Gamma_0(N)\)-optimal |
| 180336.cy2 | 180336v2 | \([0, 1, 0, -348052, -89912920]\) | \(-754612278352/127035441\) | \(-784979640981229824\) | \([2]\) | \(2211840\) | \(2.1605\) |
Rank
sage: E.rank()
The elliptic curves in class 180336.cy have rank \(1\).
Complex multiplication
The elliptic curves in class 180336.cy do not have complex multiplication.Modular form 180336.2.a.cy
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.
