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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 230384.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230384.cy1 | 230384cy2 | \([0, -1, 0, -75505008, 252553459424]\) | \(13120939360620031250/59918717089\) | \(217394508523327342592\) | \([2]\) | \(20398080\) | \(3.1062\) | |
| 230384.cy2 | 230384cy1 | \([0, -1, 0, -4642568, 4081399808]\) | \(-6100178719130500/433648016263\) | \(-786671527259030060032\) | \([2]\) | \(10199040\) | \(2.7596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230384.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 230384.cy do not have complex multiplication.Modular form 230384.2.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.
