Properties

Label 81120.g
Number of curves $4$
Conductor $81120$
CM no
Rank $0$
Graph

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

Elliptic curves in class 81120.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81120.g1 81120z4 \([0, -1, 0, -27096, -1707720]\) \(890277128/15\) \(37069893120\) \([2]\) \(147456\) \(1.1583\)  
81120.g2 81120z3 \([0, -1, 0, -6816, 192516]\) \(14172488/1875\) \(4633736640000\) \([2]\) \(147456\) \(1.1583\)  
81120.g3 81120z1 \([0, -1, 0, -1746, -24480]\) \(1906624/225\) \(69506049600\) \([2, 2]\) \(73728\) \(0.81170\) \(\Gamma_0(N)\)-optimal
81120.g4 81120z2 \([0, -1, 0, 2479, -128415]\) \(85184/405\) \(-8007096913920\) \([2]\) \(147456\) \(1.1583\)  

Rank

sage: E.rank()
 

The elliptic curves in class 81120.g have rank \(0\).

Complex multiplication

The elliptic curves in class 81120.g do not have complex multiplication.

Modular form 81120.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.