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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 64350.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64350.ep1 | 64350eh2 | \([1, -1, 1, -6598355, 6525462647]\) | \(2789222297765780449/677605500\) | \(7718350148437500\) | \([2]\) | \(1769472\) | \(2.4258\) | |
| 64350.ep2 | 64350eh1 | \([1, -1, 1, -410855, 102837647]\) | \(-673350049820449/10617750000\) | \(-120942808593750000\) | \([2]\) | \(884736\) | \(2.0792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64350.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 64350.ep do not have complex multiplication.Modular form 64350.2.a.ep
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
