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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 230640.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230640.w1 | 230640w2 | \([0, -1, 0, -43534581, 110574888381]\) | \(2612000948224/1125\) | \(3930121900528128000\) | \([]\) | \(17677440\) | \(2.9106\) | |
230640.w2 | 230640w1 | \([0, -1, 0, -635541, 92700765]\) | \(8126464/3645\) | \(12733594957711134720\) | \([]\) | \(5892480\) | \(2.3613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230640.w have rank \(0\).
Complex multiplication
The elliptic curves in class 230640.w do not have complex multiplication.Modular form 230640.2.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 LMFDB 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 LMFDB labels.