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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 31680cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31680.r1 | 31680cy1 | \([0, 0, 0, -408, -808]\) | \(10061824/5445\) | \(4064670720\) | \([2]\) | \(16384\) | \(0.53479\) | \(\Gamma_0(N)\)-optimal |
| 31680.r2 | 31680cy2 | \([0, 0, 0, 1572, -6352]\) | \(35969456/22275\) | \(-266051174400\) | \([2]\) | \(32768\) | \(0.88137\) |
Rank
sage: E.rank()
The elliptic curves in class 31680cy have rank \(0\).
Complex multiplication
The elliptic curves in class 31680cy do not have complex multiplication.Modular form 31680.2.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.
