Show commands:
SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 95550cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.o2 | 95550cu1 | \([1, 1, 0, -236450, 29416500]\) | \(6362477477/2044224\) | \(469728338625000000\) | \([2]\) | \(1658880\) | \(2.0945\) | \(\Gamma_0(N)\)-optimal |
95550.o1 | 95550cu2 | \([1, 1, 0, -3421450, 2434091500]\) | \(19276856949797/3714984\) | \(853640923078125000\) | \([2]\) | \(3317760\) | \(2.4411\) |
Rank
sage: E.rank()
The elliptic curves in class 95550cu have rank \(0\).
Complex multiplication
The elliptic curves in class 95550cu do not have complex multiplication.Modular form 95550.2.a.cu
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.