Properties

Label 182070.f
Number of curves $2$
Conductor $182070$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 182070.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.f1 182070df2 \([1, -1, 0, -14165100, 2047381056]\) \(3635924387633/2083248720\) \(180098022559602240369360\) \([2]\) \(20054016\) \(3.1520\)  
182070.f2 182070df1 \([1, -1, 0, 3521700, 253939536]\) \(55874402767/32659200\) \(-2823406193370209529600\) \([2]\) \(10027008\) \(2.8054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 182070.f have rank \(2\).

Complex multiplication

The elliptic curves in class 182070.f do not have complex multiplication.

Modular form 182070.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2 q^{11} + 4 q^{13} + q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.