Properties

Label 88935ci
Number of curves $4$
Conductor $88935$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 88935ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.v3 88935ci1 \([1, 0, 0, -1206675, 509722632]\) \(932288503609/779625\) \(162491298076886625\) \([4]\) \(1658880\) \(2.2304\) \(\Gamma_0(N)\)-optimal
88935.v2 88935ci2 \([1, 0, 0, -1473480, 267623775]\) \(1697509118089/833765625\) \(173775415998892640625\) \([2, 2]\) \(3317760\) \(2.5769\)  
88935.v4 88935ci3 \([1, 0, 0, 5374515, 2052211272]\) \(82375335041831/56396484375\) \(-11754289502089599609375\) \([2]\) \(6635520\) \(2.9235\)  
88935.v1 88935ci4 \([1, 0, 0, -12590355, -17010223350]\) \(1058993490188089/13182390375\) \(2747505177219825243375\) \([2]\) \(6635520\) \(2.9235\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.ci

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.