Properties

Label 88935ck
Number of curves $2$
Conductor $88935$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 88935ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.x1 88935ck1 \([1, 0, 0, -1147385, -470981400]\) \(2336752783/12375\) \(884674845085271625\) \([2]\) \(1612800\) \(2.2883\) \(\Gamma_0(N)\)-optimal
88935.x2 88935ck2 \([1, 0, 0, -524840, -979849683]\) \(-223648543/5671875\) \(-405475970664082828125\) \([2]\) \(3225600\) \(2.6349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 88935ck have rank \(1\).

Complex multiplication

The elliptic curves in class 88935ck do not have complex multiplication.

Modular form 88935.2.a.ck

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 3 q^{8} + q^{9} - q^{10} - q^{12} + 4 q^{13} + q^{15} - q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.