Properties

Label 576.d
Number of curves $6$
Conductor $576$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 576.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
576.d1 576d5 \([0, 0, 0, -13836, 626416]\) \(3065617154/9\) \(859963392\) \([2]\) \(512\) \(0.94368\)  
576.d2 576d3 \([0, 0, 0, -2316, -42896]\) \(28756228/3\) \(143327232\) \([2]\) \(256\) \(0.59710\)  
576.d3 576d4 \([0, 0, 0, -876, 9520]\) \(1556068/81\) \(3869835264\) \([2, 2]\) \(256\) \(0.59710\)  
576.d4 576d2 \([0, 0, 0, -156, -560]\) \(35152/9\) \(107495424\) \([2, 2]\) \(128\) \(0.25053\)  
576.d5 576d1 \([0, 0, 0, 24, -56]\) \(2048/3\) \(-2239488\) \([2]\) \(64\) \(-0.096046\) \(\Gamma_0(N)\)-optimal
576.d6 576d6 \([0, 0, 0, 564, 37744]\) \(207646/6561\) \(-626913312768\) \([2]\) \(512\) \(0.94368\)  

Rank

sage: E.rank()
 

The elliptic curves in class 576.d have rank \(0\).

Complex multiplication

The elliptic curves in class 576.d do not have complex multiplication.

Modular form 576.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.