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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 10192.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10192.h1 | 10192p2 | \([0, -1, 0, -1682, 17179]\) | \(13707167488/4826809\) | \(185426694544\) | \([]\) | \(10368\) | \(0.86343\) | |
| 10192.h2 | 10192p1 | \([0, -1, 0, -702, -6929]\) | \(997335808/169\) | \(6492304\) | \([]\) | \(3456\) | \(0.31412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10192.h have rank \(1\).
Complex multiplication
The elliptic curves in class 10192.h do not have complex multiplication.Modular form 10192.2.a.h
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.
