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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 85176.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.bo1 | 85176bg1 | \([0, 0, 0, -9796254, -11801526035]\) | \(49860882714802176/57967\) | \(120871715314896\) | \([2]\) | \(1290240\) | \(2.4165\) | \(\Gamma_0(N)\)-optimal |
| 85176.bo2 | 85176bg2 | \([0, 0, 0, -9793719, -11807939078]\) | \(-3113886554501616/3360173089\) | \(-112105131546537222912\) | \([2]\) | \(2580480\) | \(2.7631\) |
Rank
sage: E.rank()
The elliptic curves in class 85176.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 85176.bo do not have complex multiplication.Modular form 85176.2.a.bo
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.
