Properties

Label 9408.be
Number of curves $4$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 9408.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.be1 9408i3 \([0, -1, 0, -790337, -270174015]\) \(7080974546692/189\) \(1457236279296\) \([2]\) \(73728\) \(1.8477\)  
9408.be2 9408i4 \([0, -1, 0, -76897, 1010017]\) \(6522128932/3720087\) \(28682781685383168\) \([2]\) \(73728\) \(1.8477\)  
9408.be3 9408i2 \([0, -1, 0, -49457, -4198095]\) \(6940769488/35721\) \(68854414196736\) \([2, 2]\) \(36864\) \(1.5011\)  
9408.be4 9408i1 \([0, -1, 0, -1437, -135603]\) \(-2725888/64827\) \(-7809875684352\) \([2]\) \(18432\) \(1.1546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9408.be have rank \(0\).

Complex multiplication

The elliptic curves in class 9408.be do not have complex multiplication.

Modular form 9408.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.