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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 131648bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 131648.ci2 | 131648bh1 | \([0, -1, 0, -4033, -70431]\) | \(62500/17\) | \(1973717368832\) | \([2]\) | \(179200\) | \(1.0671\) | \(\Gamma_0(N)\)-optimal |
| 131648.ci1 | 131648bh2 | \([0, -1, 0, -23393, 1327361]\) | \(6097250/289\) | \(67106390540288\) | \([2]\) | \(358400\) | \(1.4137\) |
Rank
sage: E.rank()
The elliptic curves in class 131648bh have rank \(0\).
Complex multiplication
The elliptic curves in class 131648bh do not have complex multiplication.Modular form 131648.2.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 Cremona 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 Cremona labels.
