↑

Properties

Label 208098.f
Number of curves $2$
Conductor $208098$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 208098.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208098.f1 208098s2 \([1, -1, 0, -1827225684, 30074233083336]\) \(-925492188434597796818942768449/373958095272087819200664\) \(-272615451453352020197284056\) \([]\) \(106028160\) \(4.0357\)  
208098.f2 208098s1 \([1, -1, 0, 3874356, -12244356144]\) \(8822561460536124355391/93935597925332680704\) \(-68479050887567524233216\) \([]\) \(15146880\) \(3.0628\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 208098.f have rank \(1\).

Complex multiplication

The elliptic curves in class 208098.f do not have complex multiplication.

Modular form 208098.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - q^{11} - q^{14} + q^{16} - 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.