Properties

Label 35280ck
Number of curves $4$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 35280ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.fr3 35280ck1 \([0, 0, 0, -882, -9261]\) \(55296/5\) \(6861289680\) \([2]\) \(18432\) \(0.62690\) \(\Gamma_0(N)\)-optimal
35280.fr2 35280ck2 \([0, 0, 0, -3087, 55566]\) \(148176/25\) \(548903174400\) \([2, 2]\) \(36864\) \(0.97347\)  
35280.fr4 35280ck3 \([0, 0, 0, 5733, 314874]\) \(237276/625\) \(-54890317440000\) \([2]\) \(73728\) \(1.3200\)  
35280.fr1 35280ck4 \([0, 0, 0, -47187, 3945186]\) \(132304644/5\) \(439122539520\) \([2]\) \(73728\) \(1.3200\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35280ck have rank \(0\).

Complex multiplication

The elliptic curves in class 35280ck do not have complex multiplication.

Modular form 35280.2.a.ck

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{11} + 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.