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Properties

Label 95550ee
Number of curves $2$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ee1")
 
E.isogeny_class()
 

Elliptic curves in class 95550ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.fr2 95550ee1 \([1, 0, 1, 874624, 3557304398]\) \(40251338884511/2997011332224\) \(-5509302909762834000000\) \([]\) \(7902720\) \(2.8513\) \(\Gamma_0(N)\)-optimal
95550.fr1 95550ee2 \([1, 0, 1, -4501257626, 116237836311398]\) \(-5486773802537974663600129/2635437714\) \(-4844634556474781250\) \([]\) \(55319040\) \(3.8242\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550ee have rank \(1\).

Complex multiplication

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

Modular form 95550.2.a.ee

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 5 q^{11} + q^{12} - q^{13} + q^{16} - 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.