Properties

Label 74382bg
Number of curves $2$
Conductor $74382$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 74382bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74382.bj2 74382bg1 \([1, 1, 1, 189139, -10572829]\) \(6360314548472639/4097346156288\) \(-482048677941126912\) \([2]\) \(1327104\) \(2.0820\) \(\Gamma_0(N)\)-optimal
74382.bj1 74382bg2 \([1, 1, 1, -802621, -87930109]\) \(486034459476995521/253095136942032\) \(29776389766093122768\) \([2]\) \(2654208\) \(2.4286\)  

Rank

sage: E.rank()
 

The elliptic curves in class 74382bg have rank \(0\).

Complex multiplication

The elliptic curves in class 74382bg do not have complex multiplication.

Modular form 74382.2.a.bg

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