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SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 154560hy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.l4 | 154560hy1 | \([0, -1, 0, -635356, 426701350]\) | \(-443195996177646496576/971300939313403125\) | \(-62163260116057800000\) | \([2]\) | \(3440640\) | \(2.4868\) | \(\Gamma_0(N)\)-optimal |
| 154560.l3 | 154560hy2 | \([0, -1, 0, -13228201, 18507508201]\) | \(62498004782515366780864/59053556337890625\) | \(241883366760000000000\) | \([2, 2]\) | \(6881280\) | \(2.8334\) | |
| 154560.l1 | 154560hy3 | \([0, -1, 0, -211603201, 1184833483201]\) | \(31977203346157644779097608/28589809959375\) | \(936830892748800000\) | \([2]\) | \(13762560\) | \(3.1799\) | |
| 154560.l2 | 154560hy4 | \([0, -1, 0, -16338721, 9151686145]\) | \(14720683462954119927368/7416057586669921875\) | \(243009375000000000000000\) | \([2]\) | \(13762560\) | \(3.1799\) |
Rank
sage: E.rank()
The elliptic curves in class 154560hy have rank \(0\).
Complex multiplication
The elliptic curves in class 154560hy do not have complex multiplication.Modular form 154560.2.a.hy
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 Cremona 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 Cremona labels.
