Properties

Label 361920.g
Number of curves $2$
Conductor $361920$
CM no
Rank $1$
Graph

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

Elliptic curves in class 361920.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361920.g1 361920g2 \([0, -1, 0, -156884681, 659038556745]\) \(104257038399293776070517184/14532769730198987776665\) \(59526224814895053933219840\) \([2]\) \(120913920\) \(3.6721\)  
361920.g2 361920g1 \([0, -1, 0, 15833644, 55111661550]\) \(6859403317104911965087424/24475231937622520176525\) \(-1566414844007841291297600\) \([2]\) \(60456960\) \(3.3255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 361920.g have rank \(1\).

Complex multiplication

The elliptic curves in class 361920.g do not have complex multiplication.

Modular form 361920.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} + 4 q^{11} + q^{13} + q^{15} - 8 q^{19} + O(q^{20})\) 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.