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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 193200.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.dv1 | 193200bz3 | \([0, 1, 0, -71539608, 232875328788]\) | \(632678989847546725777/80515134\) | \(5152968576000000\) | \([2]\) | \(11796480\) | \(2.8749\) | |
193200.dv2 | 193200bz4 | \([0, 1, 0, -5115608, 2520208788]\) | \(231331938231569617/90942310746882\) | \(5820307887800448000000\) | \([2]\) | \(11796480\) | \(2.8749\) | |
193200.dv3 | 193200bz2 | \([0, 1, 0, -4471608, 3636904788]\) | \(154502321244119857/55101928644\) | \(3526523433216000000\) | \([2, 2]\) | \(5898240\) | \(2.5283\) | |
193200.dv4 | 193200bz1 | \([0, 1, 0, -239608, 73560788]\) | \(-23771111713777/22848457968\) | \(-1462301309952000000\) | \([2]\) | \(2949120\) | \(2.1817\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193200.dv have rank \(2\).
Complex multiplication
The elliptic curves in class 193200.dv do not have complex multiplication.Modular form 193200.2.a.dv
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.