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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 18480.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.h1 | 18480bp3 | \([0, -1, 0, -388176, 93216960]\) | \(1579250141304807889/41926500\) | \(171730944000\) | \([2]\) | \(124416\) | \(1.6699\) | |
| 18480.h2 | 18480bp4 | \([0, -1, 0, -387696, 93458496]\) | \(-1573398910560073969/8138108343750\) | \(-33333691776000000\) | \([2]\) | \(248832\) | \(2.0164\) | |
| 18480.h3 | 18480bp1 | \([0, -1, 0, -5136, 110016]\) | \(3658671062929/880165440\) | \(3605157642240\) | \([2]\) | \(41472\) | \(1.1206\) | \(\Gamma_0(N)\)-optimal |
| 18480.h4 | 18480bp2 | \([0, -1, 0, 12144, 676800]\) | \(48351870250991/76871856600\) | \(-314867124633600\) | \([2]\) | \(82944\) | \(1.4671\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.h have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.h do not have complex multiplication.Modular form 18480.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
