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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 257600o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.o3 | 257600o1 | \([0, 1, 0, -241633, 44308863]\) | \(380920459249/12622400\) | \(51701350400000000\) | \([2]\) | \(2654208\) | \(1.9801\) | \(\Gamma_0(N)\)-optimal |
| 257600.o4 | 257600o2 | \([0, 1, 0, 78367, 153428863]\) | \(12994449551/2489452840\) | \(-10196798832640000000\) | \([2]\) | \(5308416\) | \(2.3266\) | |
| 257600.o1 | 257600o3 | \([0, 1, 0, -2705633, -1699083137]\) | \(534774372149809/5323062500\) | \(21803264000000000000\) | \([2]\) | \(7962624\) | \(2.5294\) | |
| 257600.o2 | 257600o4 | \([0, 1, 0, -705633, -4153083137]\) | \(-9486391169809/1813439640250\) | \(-7427848766464000000000\) | \([2]\) | \(15925248\) | \(2.8759\) |
Rank
sage: E.rank()
The elliptic curves in class 257600o have rank \(0\).
Complex multiplication
The elliptic curves in class 257600o do not have complex multiplication.Modular form 257600.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
