Properties

Label 29400n
Number of curves $6$
Conductor $29400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.ce5 29400n1 \([0, -1, 0, 817, -11388]\) \(2048/3\) \(-88236750000\) \([2]\) \(24576\) \(0.78575\) \(\Gamma_0(N)\)-optimal
29400.ce4 29400n2 \([0, -1, 0, -5308, -109388]\) \(35152/9\) \(4235364000000\) \([2, 2]\) \(49152\) \(1.1323\)  
29400.ce3 29400n3 \([0, -1, 0, -29808, 1899612]\) \(1556068/81\) \(152473104000000\) \([2, 2]\) \(98304\) \(1.4789\)  
29400.ce2 29400n4 \([0, -1, 0, -78808, -8488388]\) \(28756228/3\) \(5647152000000\) \([2]\) \(98304\) \(1.4789\)  
29400.ce6 29400n5 \([0, -1, 0, 19192, 7485612]\) \(207646/6561\) \(-24700642848000000\) \([2]\) \(196608\) \(1.8255\)  
29400.ce1 29400n6 \([0, -1, 0, -470808, 124497612]\) \(3065617154/9\) \(33882912000000\) \([2]\) \(196608\) \(1.8255\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29400n have rank \(0\).

Complex multiplication

The elliptic curves in class 29400n do not have complex multiplication.

Modular form 29400.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.