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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 43350k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.i2 43350k1 \([1, 1, 0, -18786595, 16571903245]\) \(247336189744145/103079215104\) \(305598630754021225267200\) \([]\) \(9139200\) \(3.2035\) \(\Gamma_0(N)\)-optimal
43350.i1 43350k2 \([1, 1, 0, -5486759075, -156432971797875]\) \(15773608170290225/31104\) \(36021067485963750000000\) \([]\) \(45696000\) \(4.0082\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 43350.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 3 q^{7} - q^{8} + q^{9} + 5 q^{11} - q^{12} - 6 q^{13} + 3 q^{14} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.