Properties

Label 88935.u
Number of curves $2$
Conductor $88935$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 88935.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.u1 88935cb2 \([1, 0, 0, -9863015, -8782206168]\) \(1115157653/295245\) \(28093062027645620917065\) \([2]\) \(7096320\) \(3.0160\)  
88935.u2 88935cb1 \([1, 0, 0, 1550310, -886467933]\) \(4330747/6075\) \(-578046543778716479775\) \([2]\) \(3548160\) \(2.6695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 88935.u have rank \(0\).

Complex multiplication

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

Modular form 88935.2.a.u

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