Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5544.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5544.c1 | 5544t3 | \([0, 0, 0, -5762091, 3774890054]\) | \(14171198121996897746/4077720290568771\) | \(6088003772056850552832\) | \([2]\) | \(368640\) | \(2.8864\) | |
| 5544.c2 | 5544t2 | \([0, 0, 0, -5282931, 4673123390]\) | \(21843440425782779332/3100814593569\) | \(2314745690840884224\) | \([2, 2]\) | \(184320\) | \(2.5399\) | |
| 5544.c3 | 5544t1 | \([0, 0, 0, -5282751, 4673457794]\) | \(87364831012240243408/1760913\) | \(328628627712\) | \([4]\) | \(92160\) | \(2.1933\) | \(\Gamma_0(N)\)-optimal |
| 5544.c4 | 5544t4 | \([0, 0, 0, -4806651, 5549954870]\) | \(-8226100326647904626/4152140742401883\) | \(-6199112911280072103936\) | \([2]\) | \(368640\) | \(2.8864\) |
Rank
sage: E.rank()
The elliptic curves in class 5544.c have rank \(0\).
Complex multiplication
The elliptic curves in class 5544.c do not have complex multiplication.Modular form 5544.2.a.c
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.
