Properties

Label 124950.fy
Number of curves $2$
Conductor $124950$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("fy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 124950.fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.fy1 124950fn2 \([1, 1, 1, -635188, -143809219]\) \(15417797707369/4080067320\) \(7500247502041875000\) \([2]\) \(2654208\) \(2.3304\)  
124950.fy2 124950fn1 \([1, 1, 1, 99812, -14449219]\) \(59822347031/83966400\) \(-154352546775000000\) \([2]\) \(1327104\) \(1.9838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 124950.fy have rank \(0\).

Complex multiplication

The elliptic curves in class 124950.fy do not have complex multiplication.

Modular form 124950.2.a.fy

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 2q^{11} - q^{12} - 2q^{13} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  Toggle raw display

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.