Properties

Label 176400.rj
Number of curves $6$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("rj1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.rj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.rj1 176400gp5 \([0, 0, 0, -2963523675, 62095583898250]\) \(524388516989299201/3150\) \(17290449993600000000\) \([2]\) \(56623104\) \(3.7569\)  
176400.rj2 176400gp3 \([0, 0, 0, -185223675, 970205598250]\) \(128031684631201/9922500\) \(54464917479840000000000\) \([2, 2]\) \(28311552\) \(3.4103\)  
176400.rj3 176400gp6 \([0, 0, 0, -172875675, 1105132194250]\) \(-104094944089921/35880468750\) \(-196949031958350000000000000\) \([2]\) \(56623104\) \(3.7569\)  
176400.rj4 176400gp4 \([0, 0, 0, -65271675, -191839985750]\) \(5602762882081/345888060\) \(1898590541210576640000000\) \([2]\) \(28311552\) \(3.4103\)  
176400.rj5 176400gp2 \([0, 0, 0, -12351675, 13013334250]\) \(37966934881/8643600\) \(47444994782438400000000\) \([2, 2]\) \(14155776\) \(3.0637\)  
176400.rj6 176400gp1 \([0, 0, 0, 1760325, 1258038250]\) \(109902239/188160\) \(-1032816212951040000000\) \([2]\) \(7077888\) \(2.7172\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 176400.rj have rank \(0\).

Complex multiplication

The elliptic curves in class 176400.rj do not have complex multiplication.

Modular form 176400.2.a.rj

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.