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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14161.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14161.b1 | 14161b3 | \([1, -1, 1, -1284226, 560478440]\) | \(82483294977/17\) | \(48275934539777\) | \([2]\) | \(82944\) | \(2.0129\) | |
| 14161.b2 | 14161b2 | \([1, -1, 1, -80541, 8709236]\) | \(20346417/289\) | \(820690887176209\) | \([2, 2]\) | \(41472\) | \(1.6664\) | |
| 14161.b3 | 14161b1 | \([1, -1, 1, -9736, -155550]\) | \(35937/17\) | \(48275934539777\) | \([2]\) | \(20736\) | \(1.3198\) | \(\Gamma_0(N)\)-optimal |
| 14161.b4 | 14161b4 | \([1, -1, 1, -9736, 23436676]\) | \(-35937/83521\) | \(-237179666393924401\) | \([2]\) | \(82944\) | \(2.0129\) |
Rank
sage: E.rank()
The elliptic curves in class 14161.b have rank \(0\).
Complex multiplication
The elliptic curves in class 14161.b do not have complex multiplication.Modular form 14161.2.a.b
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.
