Properties

Label 43560.by
Number of curves $2$
Conductor $43560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 43560.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.by1 43560cc2 \([0, 0, 0, -8620887, 9742619194]\) \(161019290864/135\) \(59406700034499840\) \([2]\) \(1216512\) \(2.5214\)  
43560.by2 43560cc1 \([0, 0, 0, -535062, 154447909]\) \(-615962624/18225\) \(-501244031541092400\) \([2]\) \(608256\) \(2.1749\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43560.by have rank \(0\).

Complex multiplication

The elliptic curves in class 43560.by do not have complex multiplication.

Modular form 43560.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{13} - 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.