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Properties

Label 405042.g
Number of curves $2$
Conductor $405042$
CM no
Rank $0$
Graph

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

Elliptic curves in class 405042.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405042.g1 405042g1 \([1, 1, 0, -326351, -71327835]\) \(81706955619457/744505344\) \(35025909817688064\) \([2]\) \(6773760\) \(1.9968\) \(\Gamma_0(N)\)-optimal
405042.g2 405042g2 \([1, 1, 0, -95311, -170074331]\) \(-2035346265217/264305213568\) \(-12434471625199713408\) \([2]\) \(13547520\) \(2.3434\)  

Rank

sage: E.rank()
 

The elliptic curves in class 405042.g have rank \(0\).

Complex multiplication

The elliptic curves in class 405042.g do not have complex multiplication.

Modular form 405042.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{10} - q^{11} - q^{12} + 4 q^{13} + 4 q^{14} + 2 q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})\) 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.