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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 272734cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.cy2 | 272734cy1 | \([1, -1, 1, -48544, 19172255]\) | \(-60698457/725788\) | \(-151270462400035132\) | \([2]\) | \(2949120\) | \(1.9783\) | \(\Gamma_0(N)\)-optimal |
272734.cy1 | 272734cy2 | \([1, -1, 1, -1412214, 644278583]\) | \(1494447319737/5411854\) | \(1127951491374175006\) | \([2]\) | \(5898240\) | \(2.3249\) |
Rank
sage: E.rank()
The elliptic curves in class 272734cy have rank \(1\).
Complex multiplication
The elliptic curves in class 272734cy do not have complex multiplication.Modular form 272734.2.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.