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Properties

Label 160446bm
Number of curves $2$
Conductor $160446$
CM no
Rank $0$
Graph

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

Elliptic curves in class 160446bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.v1 160446bm1 \([1, 0, 1, -41230027, 101895545222]\) \(-36159554681206301257/125899594704\) \(-26987696239102966224\) \([3]\) \(23721984\) \(2.9479\) \(\Gamma_0(N)\)-optimal
160446.v2 160446bm2 \([1, 0, 1, -26435962, 175886114732]\) \(-9531638527140434617/56831105229410304\) \(-12182252122969641055309824\) \([]\) \(71165952\) \(3.4973\)  

Rank

sage: E.rank()
 

The elliptic curves in class 160446bm have rank \(0\).

Complex multiplication

The elliptic curves in class 160446bm do not have complex multiplication.

Modular form 160446.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} - 3 q^{10} + q^{12} + q^{13} + 4 q^{14} + 3 q^{15} + q^{16} - q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.