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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 162450cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.br4 | 162450cu1 | \([1, -1, 0, -245367, -63571959]\) | \(-24389/12\) | \(-803822982398437500\) | \([2]\) | \(2304000\) | \(2.1410\) | \(\Gamma_0(N)\)-optimal |
| 162450.br2 | 162450cu2 | \([1, -1, 0, -4306617, -3438470709]\) | \(131872229/18\) | \(1205734473597656250\) | \([2]\) | \(4608000\) | \(2.4875\) | |
| 162450.br3 | 162450cu3 | \([1, -1, 0, -2275992, 6351172416]\) | \(-19465109/248832\) | \(-16668073363014000000000\) | \([2]\) | \(11520000\) | \(2.9457\) | |
| 162450.br1 | 162450cu4 | \([1, -1, 0, -67255992, 211622992416]\) | \(502270291349/1889568\) | \(126573182100387562500000\) | \([2]\) | \(23040000\) | \(3.2923\) |
Rank
sage: E.rank()
The elliptic curves in class 162450cu have rank \(0\).
Complex multiplication
The elliptic curves in class 162450cu do not have complex multiplication.Modular form 162450.2.a.cu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
