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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 10192.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10192.bh1 | 10192t2 | \([0, 1, 0, -82434, -5727541]\) | \(13707167488/4826809\) | \(21815265186407056\) | \([]\) | \(72576\) | \(1.8364\) | |
| 10192.bh2 | 10192t1 | \([0, 1, 0, -34414, 2445463]\) | \(997335808/169\) | \(763813073296\) | \([]\) | \(24192\) | \(1.2871\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10192.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 10192.bh do not have complex multiplication.Modular form 10192.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
