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Properties

Label 88725.v
Number of curves $2$
Conductor $88725$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 88725.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88725.v1 88725cn1 \([1, 0, 0, -840018, 292850427]\) \(108647414150813/1440074181\) \(868870377189803625\) \([2]\) \(1612800\) \(2.2495\) \(\Gamma_0(N)\)-optimal
88725.v2 88725cn2 \([1, 0, 0, -125993, 774817302]\) \(-366600498893/429644853729\) \(-259226705847852595125\) \([2]\) \(3225600\) \(2.5960\)  

Rank

sage: E.rank()
 

The elliptic curves in class 88725.v have rank \(0\).

Complex multiplication

The elliptic curves in class 88725.v do not have complex multiplication.

Modular form 88725.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} + q^{9} + 6 q^{11} - q^{12} - q^{14} - q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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.