Properties

Label 46800.ee
Number of curves $4$
Conductor $46800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ee1")
 
E.isogeny_class()
 

Elliptic curves in class 46800.ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.ee1 46800dc4 \([0, 0, 0, -4305675, -3263831750]\) \(189208196468929/10860320250\) \(506699101584000000000\) \([2]\) \(1327104\) \(2.7270\)  
46800.ee2 46800dc2 \([0, 0, 0, -741675, 244764250]\) \(967068262369/4928040\) \(229922634240000000\) \([2]\) \(442368\) \(2.1777\)  
46800.ee3 46800dc1 \([0, 0, 0, -21675, 7884250]\) \(-24137569/561600\) \(-26202009600000000\) \([2]\) \(221184\) \(1.8311\) \(\Gamma_0(N)\)-optimal
46800.ee4 46800dc3 \([0, 0, 0, 194325, -208331750]\) \(17394111071/411937500\) \(-19219356000000000000\) \([2]\) \(663552\) \(2.3804\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800.ee have rank \(1\).

Complex multiplication

The elliptic curves in class 46800.ee do not have complex multiplication.

Modular form 46800.2.a.ee

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.