Properties

Label 55440.en
Number of curves $2$
Conductor $55440$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("en1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55440.en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.en1 55440ey2 \([0, 0, 0, -4647, 121714]\) \(59466754384/121275\) \(22632825600\) \([2]\) \(61440\) \(0.87338\)  
55440.en2 55440ey1 \([0, 0, 0, -192, 3211]\) \(-67108864/343035\) \(-4001160240\) \([2]\) \(30720\) \(0.52680\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55440.en have rank \(0\).

Complex multiplication

The elliptic curves in class 55440.en do not have complex multiplication.

Modular form 55440.2.a.en

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + q^{11} - 6q^{13} - 2q^{17} + O(q^{20})\)  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.