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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 148764.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148764.bh1 | 148764o2 | \([0, 1, 0, -500796, 135520692]\) | \(461188987116496/2811467307\) | \(84676177203518208\) | \([2]\) | \(2211840\) | \(2.0869\) | |
| 148764.bh2 | 148764o1 | \([0, 1, 0, -500061, 135941112]\) | \(7346581704933376/275517\) | \(518628792528\) | \([2]\) | \(1105920\) | \(1.7403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148764.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 148764.bh do not have complex multiplication.Modular form 148764.2.a.bh
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.
