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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 194350.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194350.dg1 | 194350ba2 | \([1, -1, 1, -117630, -116422003]\) | \(-68166000163521/2179088286080\) | \(-5754155005430000000\) | \([]\) | \(4346496\) | \(2.2801\) | |
194350.dg2 | 194350ba1 | \([1, -1, 1, -20130, 1114247]\) | \(-341608037121/3593750\) | \(-9489746093750\) | \([]\) | \(620928\) | \(1.3071\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 194350.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 194350.dg do not have complex multiplication.Modular form 194350.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.