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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 223440.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223440.ch1 | 223440dc4 | \([0, -1, 0, -486880, -130409600]\) | \(26487576322129/44531250\) | \(21459177600000000\) | \([2]\) | \(2359296\) | \(2.0290\) | |
| 223440.ch2 | 223440dc2 | \([0, -1, 0, -40000, -635648]\) | \(14688124849/8122500\) | \(3914153994240000\) | \([2, 2]\) | \(1179648\) | \(1.6824\) | |
| 223440.ch3 | 223440dc1 | \([0, -1, 0, -24320, 1459200]\) | \(3301293169/22800\) | \(10987098931200\) | \([2]\) | \(589824\) | \(1.3359\) | \(\Gamma_0(N)\)-optimal |
| 223440.ch4 | 223440dc3 | \([0, -1, 0, 156000, -5182848]\) | \(871257511151/527800050\) | \(-254341726545715200\) | \([2]\) | \(2359296\) | \(2.0290\) |
Rank
sage: E.rank()
The elliptic curves in class 223440.ch have rank \(2\).
Complex multiplication
The elliptic curves in class 223440.ch do not have complex multiplication.Modular form 223440.2.a.ch
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.
