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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 22050dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.db2 | 22050dx1 | \([1, -1, 1, -11255, -1057003]\) | \(-2401/6\) | \(-393988118343750\) | \([]\) | \(94080\) | \(1.4885\) | \(\Gamma_0(N)\)-optimal |
| 22050.db1 | 22050dx2 | \([1, -1, 1, -1554755, 774551747]\) | \(-6329617441/279936\) | \(-18381909649446000000\) | \([]\) | \(658560\) | \(2.4615\) |
Rank
sage: E.rank()
The elliptic curves in class 22050dx have rank \(1\).
Complex multiplication
The elliptic curves in class 22050dx do not have complex multiplication.Modular form 22050.2.a.dx
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 Cremona 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 Cremona labels.
