Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88935.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.cb1 88935s2 \([0, -1, 1, -158839886, -14567227396723]\) \(-2126464142970105856/438611057788643355\) \(-91416360597662969163474158595\) \([]\) \(172800000\) \(4.2364\)  
88935.cb2 88935s1 \([0, -1, 1, -53007236, 173973325217]\) \(-79028701534867456/16987307596875\) \(-3540535080644638438621875\) \([]\) \(34560000\) \(3.4317\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.cb

sage: E.q_eigenform(10)
 
\(q + 2q^{2} - q^{3} + 2q^{4} - q^{5} - 2q^{6} + q^{9} - 2q^{10} - 2q^{12} - 6q^{13} + q^{15} - 4q^{16} - 7q^{17} + 2q^{18} - 5q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.