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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 277440.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.ch1 | 277440ch4 | \([0, -1, 0, -573761, -92935935]\) | \(26410345352/10546875\) | \(8341943846400000000\) | \([2]\) | \(7864320\) | \(2.3288\) | |
| 277440.ch2 | 277440ch2 | \([0, -1, 0, -261641, 50576841]\) | \(20034997696/455625\) | \(45046496770560000\) | \([2, 2]\) | \(3932160\) | \(1.9822\) | |
| 277440.ch3 | 277440ch1 | \([0, -1, 0, -260196, 51172470]\) | \(1261112198464/675\) | \(1042742980800\) | \([2]\) | \(1966080\) | \(1.6357\) | \(\Gamma_0(N)\)-optimal |
| 277440.ch4 | 277440ch3 | \([0, -1, 0, 27359, 155946241]\) | \(2863288/13286025\) | \(-10508446766636236800\) | \([2]\) | \(7864320\) | \(2.3288\) |
Rank
sage: E.rank()
The elliptic curves in class 277440.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 277440.ch do not have complex multiplication.Modular form 277440.2.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.
