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Properties

Label 90506.f
Number of curves $3$
Conductor $90506$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 90506.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90506.f1 90506d3 \([1, 0, 0, -1599592, 778552384]\) \(-10730978619193/6656\) \(-280753631914496\) \([]\) \(1240272\) \(2.0932\)  
90506.f2 90506d2 \([1, 0, 0, -15737, 1513121]\) \(-10218313/17576\) \(-741365059274216\) \([]\) \(413424\) \(1.5438\)  
90506.f3 90506d1 \([1, 0, 0, 1668, -42886]\) \(12167/26\) \(-1096693874666\) \([]\) \(137808\) \(0.99454\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90506.f have rank \(1\).

Complex multiplication

The elliptic curves in class 90506.f do not have complex multiplication.

Modular form 90506.2.a.f

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.