Properties

Label 352800.ku
Number of curves $2$
Conductor $352800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ku1")
 
E.isogeny_class()
 

Elliptic curves in class 352800.ku

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.ku1 352800ku1 \([0, 0, 0, -290325, 59339000]\) \(31554496/525\) \(45027213525000000\) \([2]\) \(3538944\) \(1.9940\) \(\Gamma_0(N)\)-optimal
352800.ku2 352800ku2 \([0, 0, 0, -14700, 167384000]\) \(-64/2205\) \(-12103314995520000000\) \([2]\) \(7077888\) \(2.3406\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800.ku have rank \(1\).

Complex multiplication

The elliptic curves in class 352800.ku do not have complex multiplication.

Modular form 352800.2.a.ku

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.