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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14297.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14297.b1 | 14297a3 | \([1, -1, 0, -76268, -8087989]\) | \(82483294977/17\) | \(10111996457\) | \([2]\) | \(24192\) | \(1.3070\) | |
| 14297.b2 | 14297a2 | \([1, -1, 0, -4783, -124560]\) | \(20346417/289\) | \(171903939769\) | \([2, 2]\) | \(12096\) | \(0.96044\) | |
| 14297.b3 | 14297a4 | \([1, -1, 0, -578, -339015]\) | \(-35937/83521\) | \(-49680238593241\) | \([2]\) | \(24192\) | \(1.3070\) | |
| 14297.b4 | 14297a1 | \([1, -1, 0, -578, 2431]\) | \(35937/17\) | \(10111996457\) | \([2]\) | \(6048\) | \(0.61386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14297.b have rank \(1\).
Complex multiplication
The elliptic curves in class 14297.b do not have complex multiplication.Modular form 14297.2.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.
