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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 137280.hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137280.hh1 | 137280et4 | \([0, 1, 0, -2441505, -1469180097]\) | \(6139836723518159689/3799803150\) | \(996095596953600\) | \([2]\) | \(2359296\) | \(2.1988\) | |
| 137280.hh2 | 137280et3 | \([0, 1, 0, -343585, 44467775]\) | \(17111482619973769/6627044531250\) | \(1737239961600000000\) | \([2]\) | \(2359296\) | \(2.1988\) | |
| 137280.hh3 | 137280et2 | \([0, 1, 0, -153505, -22706497]\) | \(1525998818291689/37268302500\) | \(9769661890560000\) | \([2, 2]\) | \(1179648\) | \(1.8522\) | |
| 137280.hh4 | 137280et1 | \([0, 1, 0, 1375, -1116225]\) | \(1095912791/2055596400\) | \(-538862262681600\) | \([2]\) | \(589824\) | \(1.5057\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 137280.hh have rank \(0\).
Complex multiplication
The elliptic curves in class 137280.hh do not have complex multiplication.Modular form 137280.2.a.hh
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.
