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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 188760cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.v2 | 188760cw1 | \([0, -1, 0, 70624, 100367676]\) | \(21474271004/2412470775\) | \(-4376411277956889600\) | \([2]\) | \(3317760\) | \(2.2563\) | \(\Gamma_0(N)\)-optimal |
188760.v1 | 188760cw2 | \([0, -1, 0, -2857576, 1799894956]\) | \(711264560340098/26281975005\) | \(95355129695913584640\) | \([2]\) | \(6635520\) | \(2.6029\) |
Rank
sage: E.rank()
The elliptic curves in class 188760cw have rank \(1\).
Complex multiplication
The elliptic curves in class 188760cw do not have complex multiplication.Modular form 188760.2.a.cw
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.