Properties

Label 43560.x
Number of curves $2$
Conductor $43560$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 43560.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.x1 43560bp1 \([0, 0, 0, -61743, 5905042]\) \(104795188976/1875\) \(465743520000\) \([2]\) \(122880\) \(1.3659\) \(\Gamma_0(N)\)-optimal
43560.x2 43560bp2 \([0, 0, 0, -59763, 6301438]\) \(-23758298924/3515625\) \(-3493076400000000\) \([2]\) \(245760\) \(1.7124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43560.x have rank \(1\).

Complex multiplication

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

Modular form 43560.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} - 4 q^{13} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.