Properties

Label 9240bj
Number of curves $6$
Conductor $9240$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9240bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.bi5 9240bj1 \([0, 1, 0, 2305, 141018]\) \(84611246065664/580054565475\) \(-9280873047600\) \([4]\) \(16384\) \(1.1699\) \(\Gamma_0(N)\)-optimal
9240.bi4 9240bj2 \([0, 1, 0, -30500, 1860000]\) \(12257375872392016/1191317675625\) \(304977324960000\) \([2, 4]\) \(32768\) \(1.5165\)  
9240.bi3 9240bj3 \([0, 1, 0, -109880, -11983872]\) \(143279368983686884/22699269140625\) \(23244051600000000\) \([2, 2]\) \(65536\) \(1.8631\)  
9240.bi2 9240bj4 \([0, 1, 0, -476000, 126243600]\) \(11647843478225136004/128410942275\) \(131492804889600\) \([4]\) \(65536\) \(1.8631\)  
9240.bi1 9240bj5 \([0, 1, 0, -1684880, -842323872]\) \(258286045443018193442/8440380939375\) \(17285900163840000\) \([2]\) \(131072\) \(2.2096\)  
9240.bi6 9240bj6 \([0, 1, 0, 195040, -66381600]\) \(400647648358480318/1163177490234375\) \(-2382187500000000000\) \([2]\) \(131072\) \(2.2096\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9240bj have rank \(1\).

Complex multiplication

The elliptic curves in class 9240bj do not have complex multiplication.

Modular form 9240.2.a.bj

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.