Properties

Label 481338.cy
Number of curves $2$
Conductor $481338$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 481338.cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.cy1 481338cy1 \([1, -1, 1, -91844105, -338741481207]\) \(66342819962001390625/4812668669952\) \(6215407432652840767488\) \([2]\) \(56770560\) \(3.2329\) \(\Gamma_0(N)\)-optimal
481338.cy2 481338cy2 \([1, -1, 1, -85919945, -384336186231]\) \(-54315282059491182625/17983956399469632\) \(-23225703645807598316217408\) \([2]\) \(113541120\) \(3.5795\)  

Rank

sage: E.rank()
 

The elliptic curves in class 481338.cy have rank \(1\).

Complex multiplication

The elliptic curves in class 481338.cy do not have complex multiplication.

Modular form 481338.2.a.cy

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} + q^{13} + 4 q^{14} + q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.