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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5544.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5544.b1 | 5544e4 | \([0, 0, 0, -342291, 77079886]\) | \(2970658109581346/2139291\) | \(3193944348672\) | \([2]\) | \(32768\) | \(1.7112\) | |
| 5544.b2 | 5544e3 | \([0, 0, 0, -49251, -2498690]\) | \(8849350367426/3314597517\) | \(4948667576100864\) | \([2]\) | \(32768\) | \(1.7112\) | |
| 5544.b3 | 5544e2 | \([0, 0, 0, -21531, 1188070]\) | \(1478729816932/38900169\) | \(29038820557824\) | \([2, 2]\) | \(16384\) | \(1.3647\) | |
| 5544.b4 | 5544e1 | \([0, 0, 0, 249, 59866]\) | \(9148592/8301447\) | \(-1549249244928\) | \([2]\) | \(8192\) | \(1.0181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5544.b have rank \(0\).
Complex multiplication
The elliptic curves in class 5544.b do not have complex multiplication.Modular form 5544.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
