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Properties

Label 55470.p
Number of curves $2$
Conductor $55470$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 55470.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55470.p1 55470w2 \([1, 1, 1, -50886, 3910989]\) \(2305199161/277350\) \(1753230041640150\) \([2]\) \(413952\) \(1.6558\)  
55470.p2 55470w1 \([1, 1, 1, 4584, 316533]\) \(1685159/7740\) \(-48927349999260\) \([2]\) \(206976\) \(1.3092\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55470.p have rank \(1\).

Complex multiplication

The elliptic curves in class 55470.p do not have complex multiplication.

Modular form 55470.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} + 4 q^{13} - 4 q^{14} + q^{15} + q^{16} + q^{18} + O(q^{20})\) 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.