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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 99450dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99450.dd2 | 99450dw1 | \([1, -1, 1, -7430, 345647]\) | \(-99546915625/54454842\) | \(-24810987386250\) | \([]\) | \(235008\) | \(1.2738\) | \(\Gamma_0(N)\)-optimal |
99450.dd1 | 99450dw2 | \([1, -1, 1, -665555, 209155547]\) | \(-71559517896165625/4598568\) | \(-2095222545000\) | \([3]\) | \(705024\) | \(1.8231\) |
Rank
sage: E.rank()
The elliptic curves in class 99450dw have rank \(0\).
Complex multiplication
The elliptic curves in class 99450dw do not have complex multiplication.Modular form 99450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.