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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 5808.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5808.p1 | 5808g1 | \([0, -1, 0, -969976, -367373312]\) | \(55635379958596/24057\) | \(43641285608448\) | \([2]\) | \(80640\) | \(1.9597\) | \(\Gamma_0(N)\)-optimal |
| 5808.p2 | 5808g2 | \([0, -1, 0, -965136, -371225952]\) | \(-27403349188178/578739249\) | \(-2099756815764867072\) | \([2]\) | \(161280\) | \(2.3062\) |
Rank
sage: E.rank()
The elliptic curves in class 5808.p have rank \(0\).
Complex multiplication
The elliptic curves in class 5808.p do not have complex multiplication.Modular form 5808.2.a.p
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.
