Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 43350.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43350.o1 | 43350a2 | \([1, 1, 0, -61775, 5125125]\) | \(339630096833/47239200\) | \(3626346712500000\) | \([2]\) | \(307200\) | \(1.7120\) | |
43350.o2 | 43350a1 | \([1, 1, 0, 6225, 433125]\) | \(347428927/1244160\) | \(-95508720000000\) | \([2]\) | \(153600\) | \(1.3654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43350.o have rank \(1\).
Complex multiplication
The elliptic curves in class 43350.o do not have complex multiplication.Modular form 43350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.