Properties

Label 73034.k
Number of curves $3$
Conductor $73034$
CM no
Rank $1$
Graph

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

Elliptic curves in class 73034.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73034.k1 73034k3 \([1, 1, 1, -1290794, -564998601]\) \(-10730978619193/6656\) \(-147525987674624\) \([]\) \(909792\) \(2.0395\)  
73034.k2 73034k2 \([1, 1, 1, -12699, -1103087]\) \(-10218313/17576\) \(-389560811203304\) \([]\) \(303264\) \(1.4902\)  
73034.k3 73034k1 \([1, 1, 1, 1346, 31749]\) \(12167/26\) \(-576273389354\) \([]\) \(101088\) \(0.94092\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 73034.k have rank \(1\).

Complex multiplication

The elliptic curves in class 73034.k do not have complex multiplication.

Modular form 73034.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} + q^{8} - 2 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} + q^{13} - q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.