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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 156816.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156816.db1 | 156816by2 | \([0, 0, 0, -107811, -14877918]\) | \(-35937/4\) | \(-15425210767785984\) | \([]\) | \(1244160\) | \(1.8436\) | |
156816.db2 | 156816by1 | \([0, 0, 0, 8349, 29282]\) | \(109503/64\) | \(-37616731029504\) | \([]\) | \(414720\) | \(1.2943\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 156816.db have rank \(1\).
Complex multiplication
The elliptic curves in class 156816.db do not have complex multiplication.Modular form 156816.2.a.db
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.