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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 235200dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.dw1 | 235200dw1 | \([0, -1, 0, -3033, -57063]\) | \(140608/15\) | \(329280000000\) | \([2]\) | \(245760\) | \(0.94438\) | \(\Gamma_0(N)\)-optimal |
235200.dw2 | 235200dw2 | \([0, -1, 0, 3967, -288063]\) | \(39304/225\) | \(-39513600000000\) | \([2]\) | \(491520\) | \(1.2910\) |
Rank
sage: E.rank()
The elliptic curves in class 235200dw have rank \(1\).
Complex multiplication
The elliptic curves in class 235200dw do not have complex multiplication.Modular form 235200.2.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.