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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 155610.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155610.eu1 | 155610a3 | \([1, -1, 1, -125128967, 538778326191]\) | \(297214339265273649756432169/488484917902800\) | \(356105505151141200\) | \([2]\) | \(18874368\) | \(3.0597\) | |
| 155610.eu2 | 155610a2 | \([1, -1, 1, -7822967, 8414438991]\) | \(72629093972969564016169/93022316019360000\) | \(67813268378113440000\) | \([2, 2]\) | \(9437184\) | \(2.7131\) | |
| 155610.eu3 | 155610a4 | \([1, -1, 1, -5716967, 13045111791]\) | \(-28346090452899214800169/84418326220247182800\) | \(-61540959814560196261200\) | \([2]\) | \(18874368\) | \(3.0597\) | |
| 155610.eu4 | 155610a1 | \([1, -1, 1, -622967, 53798991]\) | \(36676733979624816169/19519718400000000\) | \(14229874713600000000\) | \([2]\) | \(4718592\) | \(2.3665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155610.eu have rank \(1\).
Complex multiplication
The elliptic curves in class 155610.eu do not have complex multiplication.Modular form 155610.2.a.eu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
