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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 227154w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227154.d2 | 227154w1 | \([1, 1, 0, -11421, 464643]\) | \(6826561273/7074\) | \(170749163106\) | \([]\) | \(766080\) | \(1.0730\) | \(\Gamma_0(N)\)-optimal |
227154.d1 | 227154w2 | \([1, 1, 0, -41766, -2806548]\) | \(333822098953/53954184\) | \(1302322839138696\) | \([]\) | \(2298240\) | \(1.6223\) |
Rank
sage: E.rank()
The elliptic curves in class 227154w have rank \(0\).
Complex multiplication
The elliptic curves in class 227154w do not have complex multiplication.Modular form 227154.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.