Properties

Label 92400.ik
Number of curves $4$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ik1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ik1 92400cq4 \([0, 1, 0, -176408, 28459188]\) \(18972782339618/396165\) \(12677280000000\) \([2]\) \(491520\) \(1.6327\)  
92400.ik2 92400cq3 \([0, 1, 0, -46408, -3440812]\) \(345431270018/41507235\) \(1328231520000000\) \([2]\) \(491520\) \(1.6327\)  
92400.ik3 92400cq2 \([0, 1, 0, -11408, 409188]\) \(10262905636/1334025\) \(21344400000000\) \([2, 2]\) \(245760\) \(1.2861\)  
92400.ik4 92400cq1 \([0, 1, 0, 1092, 34188]\) \(35969456/144375\) \(-577500000000\) \([2]\) \(122880\) \(0.93951\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.ik have rank \(0\).

Complex multiplication

The elliptic curves in class 92400.ik do not have complex multiplication.

Modular form 92400.2.a.ik

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.