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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3300.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3300.h1 | 3300c4 | \([0, -1, 0, -38908, -1591688]\) | \(1628514404944/664335375\) | \(2657341500000000\) | \([2]\) | \(20736\) | \(1.6573\) | |
| 3300.h2 | 3300c2 | \([0, -1, 0, -17908, 928312]\) | \(158792223184/16335\) | \(65340000000\) | \([2]\) | \(6912\) | \(1.1080\) | |
| 3300.h3 | 3300c1 | \([0, -1, 0, -1033, 17062]\) | \(-488095744/200475\) | \(-50118750000\) | \([2]\) | \(3456\) | \(0.76145\) | \(\Gamma_0(N)\)-optimal |
| 3300.h4 | 3300c3 | \([0, -1, 0, 7967, -185438]\) | \(223673040896/187171875\) | \(-46792968750000\) | \([2]\) | \(10368\) | \(1.3108\) |
Rank
sage: E.rank()
The elliptic curves in class 3300.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3300.h do not have complex multiplication.Modular form 3300.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
