Properties

Label 9576.t
Number of curves $4$
Conductor $9576$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9576.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9576.t1 9576v3 \([0, 0, 0, -5335419, -4743521242]\) \(22501000029889239268/3620708343\) \(2702844295216128\) \([2]\) \(196608\) \(2.3635\)  
9576.t2 9576v2 \([0, 0, 0, -334479, -73643470]\) \(22174957026242512/278654127129\) \(52003547821322496\) \([2, 2]\) \(98304\) \(2.0169\)  
9576.t3 9576v4 \([0, 0, 0, -57459, -191931010]\) \(-28104147578308/21301741002339\) \(-15901664451282054144\) \([2]\) \(196608\) \(2.3635\)  
9576.t4 9576v1 \([0, 0, 0, -39234, 1171613]\) \(572616640141312/280535480757\) \(3272165847549648\) \([2]\) \(49152\) \(1.6703\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9576.t have rank \(0\).

Complex multiplication

The elliptic curves in class 9576.t do not have complex multiplication.

Modular form 9576.2.a.t

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - q^{7} + 4 q^{11} + 2 q^{13} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.