Properties

Label 9295.b
Number of curves $4$
Conductor $9295$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 9295.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9295.b1 9295c4 \([1, -1, 1, -10003, 387456]\) \(22930509321/6875\) \(33184311875\) \([2]\) \(9216\) \(0.99681\)  
9295.b2 9295c3 \([1, -1, 1, -4933, -129008]\) \(2749884201/73205\) \(353346552845\) \([2]\) \(9216\) \(0.99681\)  
9295.b3 9295c2 \([1, -1, 1, -708, 4502]\) \(8120601/3025\) \(14601097225\) \([2, 2]\) \(4608\) \(0.65024\)  
9295.b4 9295c1 \([1, -1, 1, 137, 446]\) \(59319/55\) \(-265474495\) \([2]\) \(2304\) \(0.30366\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9295.b have rank \(0\).

Complex multiplication

The elliptic curves in class 9295.b do not have complex multiplication.

Modular form 9295.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} - 3 q^{9} + q^{10} + q^{11} - q^{16} + 6 q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.