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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 298116cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298116.cy2 | 298116cy1 | \([0, 0, 0, -695604, -184624895]\) | \(16384/3\) | \(6815712137524604496\) | \([2]\) | \(5806080\) | \(2.3324\) | \(\Gamma_0(N)\)-optimal |
| 298116.cy1 | 298116cy2 | \([0, 0, 0, -3304119, 2141648782]\) | \(109744/9\) | \(327154182601181015808\) | \([2]\) | \(11612160\) | \(2.6790\) |
Rank
sage: E.rank()
The elliptic curves in class 298116cy have rank \(0\).
Complex multiplication
The elliptic curves in class 298116cy do not have complex multiplication.Modular form 298116.2.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 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.
