Properties

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

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Show commands: SageMath
E = EllipticCurve("ix1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.ix1 176400jz4 \([0, 0, 0, -4663575, -1553532750]\) \(1210991472/588245\) \(5448761119545660000000\) \([2]\) \(7962624\) \(2.8643\)  
176400.ix2 176400jz3 \([0, 0, 0, -3836700, -2890589625]\) \(10788913152/8575\) \(4964250291131250000\) \([2]\) \(3981312\) \(2.5177\)  
176400.ix3 176400jz2 \([0, 0, 0, -2458575, 1483732250]\) \(129348709488/6125\) \(77824813500000000\) \([2]\) \(2654208\) \(2.3150\)  
176400.ix4 176400jz1 \([0, 0, 0, -161700, 20622875]\) \(588791808/109375\) \(86858050781250000\) \([2]\) \(1327104\) \(1.9684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 176400.2.a.ix

sage: E.q_eigenform(10)
 
\(q - 4 q^{13} + 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.