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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 414050.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 414050.x1 | 414050x1 | \([1, 1, 0, -3420225, 2559647875]\) | \(-226981/14\) | \(-272914413348079343750\) | \([]\) | \(19169280\) | \(2.6757\) | \(\Gamma_0(N)\)-optimal |
| 414050.x2 | 414050x2 | \([1, 1, 0, 10036400, -155300020000]\) | \(5735339/537824\) | \(-10484280103179816069500000\) | \([]\) | \(95846400\) | \(3.4804\) |
Rank
sage: E.rank()
The elliptic curves in class 414050.x have rank \(1\).
Complex multiplication
The elliptic curves in class 414050.x do not have complex multiplication.Modular form 414050.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
