Properties

Label 23520.g
Number of curves $4$
Conductor $23520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 23520.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.g1 23520bd4 \([0, -1, 0, -7856, -265404]\) \(890277128/15\) \(903544320\) \([2]\) \(24576\) \(0.84876\)  
23520.g2 23520bd3 \([0, -1, 0, -1976, 30360]\) \(14172488/1875\) \(112943040000\) \([2]\) \(24576\) \(0.84876\)  
23520.g3 23520bd1 \([0, -1, 0, -506, -3744]\) \(1906624/225\) \(1694145600\) \([2, 2]\) \(12288\) \(0.50218\) \(\Gamma_0(N)\)-optimal
23520.g4 23520bd2 \([0, -1, 0, 719, -20159]\) \(85184/405\) \(-195165573120\) \([2]\) \(24576\) \(0.84876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.g have rank \(1\).

Complex multiplication

The elliptic curves in class 23520.g do not have complex multiplication.

Modular form 23520.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.