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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 70560.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.eh1 | 70560bx1 | \([0, 0, 0, -604317, 180818624]\) | \(4446542056384/25725\) | \(141205341614400\) | \([2]\) | \(737280\) | \(1.9055\) | \(\Gamma_0(N)\)-optimal |
| 70560.eh2 | 70560bx2 | \([0, 0, 0, -593292, 187733504]\) | \(-65743598656/5294205\) | \(-1859843795471585280\) | \([2]\) | \(1474560\) | \(2.2520\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 70560.eh do not have complex multiplication.Modular form 70560.2.a.eh
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.
