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Properties

Label 43350.ci
Number of curves $4$
Conductor $43350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 43350.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.ci1 43350cn4 \([1, 1, 1, -239298, 44810031]\) \(502270291349/1889568\) \(5701197247524000\) \([2]\) \(409600\) \(1.8826\)  
43350.ci2 43350cn2 \([1, 1, 1, -15323, -736369]\) \(131872229/18\) \(54309530250\) \([2]\) \(81920\) \(1.0779\)  
43350.ci3 43350cn3 \([1, 1, 1, -8098, 1344431]\) \(-19465109/248832\) \(-750774946176000\) \([2]\) \(204800\) \(1.5361\)  
43350.ci4 43350cn1 \([1, 1, 1, -873, -13869]\) \(-24389/12\) \(-36206353500\) \([2]\) \(40960\) \(0.73134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43350.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 43350.ci do not have complex multiplication.

Modular form 43350.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 2 q^{7} + q^{8} + q^{9} - 2 q^{11} - q^{12} - 6 q^{13} + 2 q^{14} + q^{16} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.