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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 61200bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.bq1 | 61200bw1 | \([0, 0, 0, -975, 4750]\) | \(35152/17\) | \(49572000000\) | \([2]\) | \(49152\) | \(0.74582\) | \(\Gamma_0(N)\)-optimal |
61200.bq2 | 61200bw2 | \([0, 0, 0, 3525, 36250]\) | \(415292/289\) | \(-3370896000000\) | \([2]\) | \(98304\) | \(1.0924\) |
Rank
sage: E.rank()
The elliptic curves in class 61200bw have rank \(1\).
Complex multiplication
The elliptic curves in class 61200bw do not have complex multiplication.Modular form 61200.2.a.bw
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.