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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 75504cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75504.ci4 | 75504cn1 | \([0, 1, 0, 928, -22860]\) | \(12167/39\) | \(-282996240384\) | \([2]\) | \(81920\) | \(0.88058\) | \(\Gamma_0(N)\)-optimal |
| 75504.ci3 | 75504cn2 | \([0, 1, 0, -8752, -274540]\) | \(10218313/1521\) | \(11036853374976\) | \([2, 2]\) | \(163840\) | \(1.2272\) | |
| 75504.ci2 | 75504cn3 | \([0, 1, 0, -37792, 2548148]\) | \(822656953/85683\) | \(621742740123648\) | \([2]\) | \(327680\) | \(1.5737\) | |
| 75504.ci1 | 75504cn4 | \([0, 1, 0, -134592, -19049868]\) | \(37159393753/1053\) | \(7640898490368\) | \([2]\) | \(327680\) | \(1.5737\) |
Rank
sage: E.rank()
The elliptic curves in class 75504cn have rank \(0\).
Complex multiplication
The elliptic curves in class 75504cn do not have complex multiplication.Modular form 75504.2.a.cn
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.
