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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 85176.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.be1 | 85176k2 | \([0, 0, 0, -15795, -757458]\) | \(4920750/49\) | \(4339576829952\) | \([2]\) | \(156672\) | \(1.2435\) | |
| 85176.be2 | 85176k1 | \([0, 0, 0, -1755, 9126]\) | \(13500/7\) | \(309969773568\) | \([2]\) | \(78336\) | \(0.89695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.be have rank \(1\).
Complex multiplication
The elliptic curves in class 85176.be do not have complex multiplication.Modular form 85176.2.a.be
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.
