Properties

Label 576.g
Number of curves $4$
Conductor $576$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 576.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
576.g1 576c3 \([0, 0, 0, -1164, -15280]\) \(7301384/3\) \(71663616\) \([2]\) \(256\) \(0.46966\)  
576.g2 576c2 \([0, 0, 0, -84, -160]\) \(21952/9\) \(26873856\) \([2, 2]\) \(128\) \(0.12309\)  
576.g3 576c1 \([0, 0, 0, -39, 92]\) \(140608/3\) \(139968\) \([2]\) \(64\) \(-0.22349\) \(\Gamma_0(N)\)-optimal
576.g4 576c4 \([0, 0, 0, 276, -1168]\) \(97336/81\) \(-1934917632\) \([2]\) \(256\) \(0.46966\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 576.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.