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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 89280cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.fx2 | 89280cy1 | \([0, 0, 0, -7860972, -8495449936]\) | \(-281115640967896441/468084326400\) | \(-89452307793995366400\) | \([2]\) | \(3194880\) | \(2.7242\) | \(\Gamma_0(N)\)-optimal |
| 89280.fx1 | 89280cy2 | \([0, 0, 0, -125825772, -543253481296]\) | \(1152829477932246539641/3188367360\) | \(609306491077263360\) | \([2]\) | \(6389760\) | \(3.0708\) |
Rank
sage: E.rank()
The elliptic curves in class 89280cy have rank \(0\).
Complex multiplication
The elliptic curves in class 89280cy do not have complex multiplication.Modular form 89280.2.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.
