Properties

Label 95550s
Number of curves $2$
Conductor $95550$
CM no
Rank $2$
Graph

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

Elliptic curves in class 95550s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.v1 95550s1 \([1, 1, 0, -281775, -13966875]\) \(1345938541921/733824000\) \(1348963434000000000\) \([2]\) \(2211840\) \(2.1696\) \(\Gamma_0(N)\)-optimal
95550.v2 95550s2 \([1, 1, 0, 1090225, -108634875]\) \(77958456780959/47911500000\) \(-88074063492187500000\) \([2]\) \(4423680\) \(2.5162\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550s have rank \(2\).

Complex multiplication

The elliptic curves in class 95550s do not have complex multiplication.

Modular form 95550.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 2 q^{11} - q^{12} - q^{13} + q^{16} - 8 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.