Properties

Label 12880.u
Number of curves $4$
Conductor $12880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 12880.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12880.u1 12880n3 \([0, -1, 0, -27056, 1707200]\) \(534774372149809/5323062500\) \(21803264000000\) \([2]\) \(41472\) \(1.3781\)  
12880.u2 12880n4 \([0, -1, 0, -7056, 4155200]\) \(-9486391169809/1813439640250\) \(-7427848766464000\) \([2]\) \(82944\) \(1.7246\)  
12880.u3 12880n1 \([0, -1, 0, -2416, -43584]\) \(380920459249/12622400\) \(51701350400\) \([2]\) \(13824\) \(0.82876\) \(\Gamma_0(N)\)-optimal
12880.u4 12880n2 \([0, -1, 0, 784, -153664]\) \(12994449551/2489452840\) \(-10196798832640\) \([2]\) \(27648\) \(1.1753\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12880.u have rank \(1\).

Complex multiplication

The elliptic curves in class 12880.u do not have complex multiplication.

Modular form 12880.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} - q^{7} + q^{9} + 2 q^{13} - 2 q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.