Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 6498.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6498.t1 | 6498v3 | \([1, -1, 1, -1390640, -630851601]\) | \(8671983378625/82308\) | \(2822871980170692\) | \([2]\) | \(103680\) | \(2.1270\) | |
6498.t2 | 6498v4 | \([1, -1, 1, -1358150, -661756089]\) | \(-8078253774625/846825858\) | \(-29043118367986164642\) | \([2]\) | \(207360\) | \(2.4736\) | |
6498.t3 | 6498v1 | \([1, -1, 1, -26060, 130191]\) | \(57066625/32832\) | \(1126020956079168\) | \([2]\) | \(34560\) | \(1.5777\) | \(\Gamma_0(N)\)-optimal |
6498.t4 | 6498v2 | \([1, -1, 1, 103900, 961935]\) | \(3616805375/2105352\) | \(-72206093808576648\) | \([2]\) | \(69120\) | \(1.9243\) |
Rank
sage: E.rank()
The elliptic curves in class 6498.t have rank \(0\).
Complex multiplication
The elliptic curves in class 6498.t do not have complex multiplication.Modular form 6498.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.