Properties

Label 8400.y
Number of curves $4$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 8400.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.y1 8400f3 \([0, -1, 0, -100808, -12285888]\) \(7080974546692/189\) \(3024000000\) \([2]\) \(24576\) \(1.3329\)  
8400.y2 8400f4 \([0, -1, 0, -9808, 48112]\) \(6522128932/3720087\) \(59521392000000\) \([2]\) \(24576\) \(1.3329\)  
8400.y3 8400f2 \([0, -1, 0, -6308, -189888]\) \(6940769488/35721\) \(142884000000\) \([2, 2]\) \(12288\) \(0.98633\)  
8400.y4 8400f1 \([0, -1, 0, -183, -6138]\) \(-2725888/64827\) \(-16206750000\) \([2]\) \(6144\) \(0.63976\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8400.y have rank \(0\).

Complex multiplication

The elliptic curves in class 8400.y do not have complex multiplication.

Modular form 8400.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.