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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 96600.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.h1 | 96600c4 | \([0, -1, 0, -474808, -125734388]\) | \(369937818893666/123409881\) | \(3949116192000000\) | \([2]\) | \(1048576\) | \(1.9654\) | |
| 96600.h2 | 96600c3 | \([0, -1, 0, -240808, 44581612]\) | \(48260105780546/1193313807\) | \(38186041824000000\) | \([2]\) | \(1048576\) | \(1.9654\) | |
| 96600.h3 | 96600c2 | \([0, -1, 0, -33808, -1372388]\) | \(267100692772/102880449\) | \(1646087184000000\) | \([2, 2]\) | \(524288\) | \(1.6188\) | |
| 96600.h4 | 96600c1 | \([0, -1, 0, 6692, -157388]\) | \(8284506032/7394247\) | \(-29576988000000\) | \([2]\) | \(262144\) | \(1.2722\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.h have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.h do not have complex multiplication.Modular form 96600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
