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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 303450dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.dw2 | 303450dw1 | \([1, 1, 1, -12163438, -42702480469]\) | \(-527690404915129/1782829440000\) | \(-672393259737990000000000\) | \([2]\) | \(53084160\) | \(3.2583\) | \(\Gamma_0(N)\)-optimal |
303450.dw1 | 303450dw2 | \([1, 1, 1, -272263438, -1727110080469]\) | \(5918043195362419129/8515734343200\) | \(3211705082729057512500000\) | \([2]\) | \(106168320\) | \(3.6048\) |
Rank
sage: E.rank()
The elliptic curves in class 303450dw have rank \(0\).
Complex multiplication
The elliptic curves in class 303450dw do not have complex multiplication.Modular form 303450.2.a.dw
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.