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Properties

Label 43350.u
Number of curves $2$
Conductor $43350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 43350.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.u1 43350f2 \([1, 1, 0, -5693450, -5707888500]\) \(-17624225/1944\) \(-2251316717872734375000\) \([]\) \(2448000\) \(2.8348\)  
43350.u2 43350f1 \([1, 1, 0, 5630, 25975540]\) \(6655/98304\) \(-291441565279027200\) \([]\) \(489600\) \(2.0300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 43350.2.a.u

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.