Properties

Label 98736bm
Number of curves $2$
Conductor $98736$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 98736bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98736.bb2 98736bm1 \([0, -1, 0, -16340408, -25417950864]\) \(88506348541062171875/2094601863168\) \(11419300167174586368\) \([2]\) \(3483648\) \(2.7684\) \(\Gamma_0(N)\)-optimal
98736.bb1 98736bm2 \([0, -1, 0, -261445048, -1627029710480]\) \(362515826352179162139875/203046912\) \(1106966281715712\) \([2]\) \(6967296\) \(3.1149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 98736bm have rank \(0\).

Complex multiplication

The elliptic curves in class 98736bm do not have complex multiplication.

Modular form 98736.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} + 4 q^{13} - q^{17} + O(q^{20})\) 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.