Properties

Label 92736bt
Number of curves $2$
Conductor $92736$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 92736bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.df2 92736bt1 \([0, 0, 0, 150900, -3330448]\) \(7953970437500/4703287687\) \(-224703068492464128\) \([2]\) \(737280\) \(2.0188\) \(\Gamma_0(N)\)-optimal
92736.df1 92736bt2 \([0, 0, 0, -610860, -26792656]\) \(263822189935250/149429406721\) \(14278202163148750848\) \([2]\) \(1474560\) \(2.3654\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92736bt have rank \(1\).

Complex multiplication

The elliptic curves in class 92736bt do not have complex multiplication.

Modular form 92736.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{7} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.