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Properties

Label 324870.bu
Number of curves $2$
Conductor $324870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 324870.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.bu1 324870bu2 \([1, 0, 1, -190489, 30209036]\) \(6497434355239801/405606692400\) \(47719221754167600\) \([2]\) \(4128768\) \(1.9517\)  
324870.bu2 324870bu1 \([1, 0, 1, 9431, 1980332]\) \(788632918919/14845259520\) \(-1746529937268480\) \([2]\) \(2064384\) \(1.6051\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 324870.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 324870.bu do not have complex multiplication.

Modular form 324870.2.a.bu

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.