Properties

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

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 88935n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.k1 88935n1 \([1, 1, 1, -23416, 1363088]\) \(2336752783/12375\) \(7519612109625\) \([2]\) \(230400\) \(1.3154\) \(\Gamma_0(N)\)-optimal
88935.k2 88935n2 \([1, 1, 1, -10711, 2852114]\) \(-223648543/5671875\) \(-3446488883578125\) \([2]\) \(460800\) \(1.6620\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.n

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.