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SageMath
E = EllipticCurve("ns1")
E.isogeny_class()
Elliptic curves in class 242550.ns
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.ns1 | 242550ns4 | \([1, -1, 1, -155816555, -748540697803]\) | \(312196988566716625/25367712678\) | \(33995161172415344343750\) | \([2]\) | \(31850496\) | \(3.3685\) | |
| 242550.ns2 | 242550ns3 | \([1, -1, 1, -9073805, -13359520303]\) | \(-61653281712625/21875235228\) | \(-29314907366689227937500\) | \([2]\) | \(15925248\) | \(3.0220\) | |
| 242550.ns3 | 242550ns2 | \([1, -1, 1, -4002305, 1546720697]\) | \(5290763640625/2291573592\) | \(3070927780810572375000\) | \([2]\) | \(10616832\) | \(2.8192\) | |
| 242550.ns4 | 242550ns1 | \([1, -1, 1, 848695, 178738697]\) | \(50447927375/39517632\) | \(-52957406371023000000\) | \([2]\) | \(5308416\) | \(2.4727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.ns have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.ns do not have complex multiplication.Modular form 242550.2.a.ns
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
