Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 88935o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.n4 88935o1 \([1, 1, 1, -18720941, 2122554314]\) \(3481467828171481/2005331497785\) \(417955963635788931602865\) \([2]\) \(11059200\) \(3.2220\) \(\Gamma_0(N)\)-optimal
88935.n2 88935o2 \([1, 1, 1, -213221786, 1195424138558]\) \(5143681768032498601/14238434358225\) \(2967608377682247733382025\) \([2, 2]\) \(22118400\) \(3.5686\)  
88935.n3 88935o3 \([1, 1, 1, -129178211, 2147503373588]\) \(-1143792273008057401/8897444448004035\) \(-1854426548562659780175659115\) \([2]\) \(44236800\) \(3.9152\)  
88935.n1 88935o4 \([1, 1, 1, -3409278881, 76618536312044]\) \(21026497979043461623321/161783881875\) \(33719381720425127986875\) \([2]\) \(44236800\) \(3.9152\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.