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Properties

Label 30926.f
Number of curves $2$
Conductor $30926$
CM no
Rank $0$
Graph

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

Elliptic curves in class 30926.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30926.f1 30926d2 \([1, 1, 0, -109391, 13081661]\) \(13430356633/865928\) \(9334024371410312\) \([2]\) \(317952\) \(1.8147\)  
30926.f2 30926d1 \([1, 1, 0, -21031, -932235]\) \(95443993/21056\) \(226967157967424\) \([2]\) \(158976\) \(1.4681\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30926.f have rank \(0\).

Complex multiplication

The elliptic curves in class 30926.f do not have complex multiplication.

Modular form 30926.2.a.f

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.