↑

Properties

Label 35910.by
Number of curves $3$
Conductor $35910$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 35910.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35910.by1 35910bt3 \([1, -1, 1, -3606647, 2637610319]\) \(-21351492553819653671547/3336704000000000\) \(-810819072000000000\) \([9]\) \(1259712\) \(2.4475\)  
35910.by2 35910bt2 \([1, -1, 1, -92612, -317744909]\) \(-4463030066755707/2213637606763940\) \(-43571029013934631020\) \([]\) \(1259712\) \(2.4475\)  
35910.by3 35910bt1 \([1, -1, 1, 10288, 11754611]\) \(4460590852694397/2214283123304000\) \(-59785644329208000\) \([3]\) \(419904\) \(1.8982\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35910.by have rank \(1\).

Complex multiplication

The elliptic curves in class 35910.by do not have complex multiplication.

Modular form 35910.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 6 q^{11} - 4 q^{13} + q^{14} + q^{16} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.