Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 6336.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6336.o1 | 6336ck4 | \([0, 0, 0, -25356, 1554064]\) | \(37736227588/33\) | \(1576599552\) | \([2]\) | \(12288\) | \(1.0652\) | |
6336.o2 | 6336ck3 | \([0, 0, 0, -3756, -54704]\) | \(122657188/43923\) | \(2098454003712\) | \([2]\) | \(12288\) | \(1.0652\) | |
6336.o3 | 6336ck2 | \([0, 0, 0, -1596, 23920]\) | \(37642192/1089\) | \(13006946304\) | \([2, 2]\) | \(6144\) | \(0.71863\) | |
6336.o4 | 6336ck1 | \([0, 0, 0, 24, 1240]\) | \(2048/891\) | \(-665127936\) | \([2]\) | \(3072\) | \(0.37205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6336.o have rank \(2\).
Complex multiplication
The elliptic curves in class 6336.o do not have complex multiplication.Modular form 6336.2.a.o
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.