Properties

Label 114444p
Number of curves 2
Conductor 114444
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("114444.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 114444p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114444.p2 114444p1 [0, 0, 0, 6936, 122825] [2] 236544 \(\Gamma_0(N)\)-optimal
114444.p1 114444p2 [0, 0, 0, -32079, 1051382] [2] 473088  

Rank

sage: E.rank()
 

The elliptic curves in class 114444p have rank \(0\).

Modular form 114444.2.a.p

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 2q^{7} + q^{11} - 2q^{13} - 6q^{19} + O(q^{20}) \)

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.