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Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 88725.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88725.s1 88725cl1 \([1, 0, 0, -414138, -96971733]\) \(833237621/51597\) \(486423562447265625\) \([2]\) \(1290240\) \(2.1454\) \(\Gamma_0(N)\)-optimal
88725.s2 88725cl2 \([1, 0, 0, 325237, -405291108]\) \(403583419/7761663\) \(-73172001608138671875\) \([2]\) \(2580480\) \(2.4920\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88725.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{12} - q^{14} - q^{16} + 6 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.