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Properties

Label 16562bm
Number of curves $3$
Conductor $16562$
CM no
Rank $1$
Graph

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

Elliptic curves in class 16562bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.bd3 16562bm1 \([1, 1, 1, 3968, -156213]\) \(12167/26\) \(-14764600553066\) \([]\) \(42336\) \(1.2112\) \(\Gamma_0(N)\)-optimal
16562.bd2 16562bm2 \([1, 1, 1, -37437, 5541115]\) \(-10218313/17576\) \(-9980869973872616\) \([]\) \(127008\) \(1.7605\)  
16562.bd1 16562bm3 \([1, 1, 1, -3805292, 2855546637]\) \(-10730978619193/6656\) \(-3779737741584896\) \([]\) \(381024\) \(2.3098\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16562bm have rank \(1\).

Complex multiplication

The elliptic curves in class 16562bm do not have complex multiplication.

Modular form 16562.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{8} - 2 q^{9} - 3 q^{10} - 6 q^{11} - q^{12} + 3 q^{15} + q^{16} + 3 q^{17} - 2 q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.