Properties

Label 176400jj
Number of curves $4$
Conductor $176400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("jj1")
 
E.isogeny_class()
 

Elliptic curves in class 176400jj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.d4 176400jj1 \([0, 0, 0, 113925, 4030250]\) \(804357/500\) \(-101648736000000000\) \([2]\) \(1658880\) \(1.9525\) \(\Gamma_0(N)\)-optimal
176400.d3 176400jj2 \([0, 0, 0, -474075, 32842250]\) \(57960603/31250\) \(6353046000000000000\) \([2]\) \(3317760\) \(2.2990\)  
176400.d2 176400jj3 \([0, 0, 0, -1356075, -692259750]\) \(-1860867/320\) \(-47425234268160000000\) \([2]\) \(4976640\) \(2.5018\)  
176400.d1 176400jj4 \([0, 0, 0, -22524075, -41144307750]\) \(8527173507/200\) \(29640771417600000000\) \([2]\) \(9953280\) \(2.8483\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400jj have rank \(1\).

Complex multiplication

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

Modular form 176400.2.a.jj

sage: E.q_eigenform(10)
 
\(q - 6 q^{11} - 4 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.