Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 60690.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60690.o1 | 60690n2 | \([1, 1, 0, -387354942, 2293131936996]\) | \(54201427552325291993/12208015311282000\) | \(1447722612007794826739154000\) | \([2]\) | \(35094528\) | \(3.9245\) | |
60690.o2 | 60690n1 | \([1, 1, 0, 54815058, 221034882996]\) | \(153597108917748007/266827932000000\) | \(-31642557845965914204000000\) | \([2]\) | \(17547264\) | \(3.5779\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60690.o have rank \(0\).
Complex multiplication
The elliptic curves in class 60690.o do not have complex multiplication.Modular form 60690.2.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.