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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 224400dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.v2 | 224400dh1 | \([0, -1, 0, 352, 139392]\) | \(9393931/16427202\) | \(-8410727424000\) | \([]\) | \(422400\) | \(1.1590\) | \(\Gamma_0(N)\)-optimal |
| 224400.v1 | 224400dh2 | \([0, -1, 0, -180048, -31699008]\) | \(-1260727040508389/121448888352\) | \(-62181830836224000\) | \([]\) | \(2112000\) | \(1.9637\) |
Rank
sage: E.rank()
The elliptic curves in class 224400dh have rank \(0\).
Complex multiplication
The elliptic curves in class 224400dh do not have complex multiplication.Modular form 224400.2.a.dh
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
