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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 224400.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.cw1 | 224400fh4 | \([0, -1, 0, -4787408, -4030202688]\) | \(189602977175292169/1402500\) | \(89760000000000\) | \([2]\) | \(4718592\) | \(2.2724\) | |
| 224400.cw2 | 224400fh3 | \([0, -1, 0, -419408, -7610688]\) | \(127483771761289/73369857660\) | \(4695670890240000000\) | \([4]\) | \(4718592\) | \(2.2724\) | |
| 224400.cw3 | 224400fh2 | \([0, -1, 0, -299408, -62810688]\) | \(46380496070089/125888400\) | \(8056857600000000\) | \([2, 2]\) | \(2359296\) | \(1.9258\) | |
| 224400.cw4 | 224400fh1 | \([0, -1, 0, -11408, -1754688]\) | \(-2565726409/19388160\) | \(-1240842240000000\) | \([2]\) | \(1179648\) | \(1.5792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.cw do not have complex multiplication.Modular form 224400.2.a.cw
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
