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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 193200dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.n1 | 193200dg1 | \([0, -1, 0, -6333, -194463]\) | \(-280944640/4347\) | \(-434700000000\) | \([]\) | \(311040\) | \(1.0353\) | \(\Gamma_0(N)\)-optimal |
193200.n2 | 193200dg2 | \([0, -1, 0, 23667, -974463]\) | \(14660034560/12519843\) | \(-1251984300000000\) | \([]\) | \(933120\) | \(1.5846\) |
Rank
sage: E.rank()
The elliptic curves in class 193200dg have rank \(0\).
Complex multiplication
The elliptic curves in class 193200dg do not have complex multiplication.Modular form 193200.2.a.dg
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.