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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 54096.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.ch1 | 54096cq4 | \([0, 1, 0, -1188928568, -15702966856620]\) | \(385693937170561837203625/2159357734550274048\) | \(1040573555147182864274030592\) | \([2]\) | \(33177600\) | \(4.0265\) | |
| 54096.ch2 | 54096cq2 | \([0, 1, 0, -87804488, 301696212852]\) | \(155355156733986861625/8291568305839392\) | \(3995626371537709586055168\) | \([2]\) | \(11059200\) | \(3.4772\) | |
| 54096.ch3 | 54096cq3 | \([0, 1, 0, -32873528, -517490273196]\) | \(-8152944444844179625/235342826399858688\) | \(-113409426158047128717361152\) | \([2]\) | \(16588800\) | \(3.6799\) | |
| 54096.ch4 | 54096cq1 | \([0, 1, 0, 3641272, 18836188020]\) | \(11079872671250375/324440155855872\) | \(-156344565335193538265088\) | \([2]\) | \(5529600\) | \(3.1306\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54096.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 54096.ch do not have complex multiplication.Modular form 54096.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
