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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 13950.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13950.ch1 | 13950cc3 | \([1, -1, 1, -74405, -7793153]\) | \(3999236143617/62\) | \(706218750\) | \([2]\) | \(32768\) | \(1.2459\) | |
| 13950.ch2 | 13950cc4 | \([1, -1, 1, -6905, 9847]\) | \(3196010817/1847042\) | \(21038962781250\) | \([2]\) | \(32768\) | \(1.2459\) | |
| 13950.ch3 | 13950cc2 | \([1, -1, 1, -4655, -120653]\) | \(979146657/3844\) | \(43785562500\) | \([2, 2]\) | \(16384\) | \(0.89937\) | |
| 13950.ch4 | 13950cc1 | \([1, -1, 1, -155, -3653]\) | \(-35937/496\) | \(-5649750000\) | \([2]\) | \(8192\) | \(0.55280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13950.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 13950.ch do not have complex multiplication.Modular form 13950.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
