Properties

Label 9360.o
Number of curves $8$
Conductor $9360$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9360.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.o1 9360bm7 \([0, 0, 0, -18720003, -31175037502]\) \(242970740812818720001/24375\) \(72783360000\) \([2]\) \(196608\) \(2.4319\)  
9360.o2 9360bm5 \([0, 0, 0, -1170003, -487107502]\) \(59319456301170001/594140625\) \(1774094400000000\) \([2, 2]\) \(98304\) \(2.0853\)  
9360.o3 9360bm8 \([0, 0, 0, -1141923, -511598878]\) \(-55150149867714721/5950927734375\) \(-17769375000000000000\) \([2]\) \(196608\) \(2.4319\)  
9360.o4 9360bm3 \([0, 0, 0, -74883, -7225918]\) \(15551989015681/1445900625\) \(4317436131840000\) \([2, 2]\) \(49152\) \(1.7387\)  
9360.o5 9360bm2 \([0, 0, 0, -16563, 693938]\) \(168288035761/27720225\) \(82772148326400\) \([2, 2]\) \(24576\) \(1.3921\)  
9360.o6 9360bm1 \([0, 0, 0, -15843, 767522]\) \(147281603041/5265\) \(15721205760\) \([2]\) \(12288\) \(1.0456\) \(\Gamma_0(N)\)-optimal
9360.o7 9360bm4 \([0, 0, 0, 30237, 3904418]\) \(1023887723039/2798036865\) \(-8354893310300160\) \([2]\) \(49152\) \(1.7387\)  
9360.o8 9360bm6 \([0, 0, 0, 87117, -34215118]\) \(24487529386319/183539412225\) \(-548045748273254400\) \([2]\) \(98304\) \(2.0853\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9360.o have rank \(0\).

Complex multiplication

The elliptic curves in class 9360.o do not have complex multiplication.

Modular form 9360.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{11} + q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.