Properties

Label 40560.j
Number of curves $2$
Conductor $40560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 40560.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.j1 40560bh2 \([0, -1, 0, -8694261, 12182645565]\) \(-21752792449024/6591796875\) \(-22024729467000000000000\) \([]\) \(3234816\) \(3.0011\)  
40560.j2 40560bh1 \([0, -1, 0, 796779, -142418979]\) \(16742875136/12301875\) \(-41103431120494080000\) \([]\) \(1078272\) \(2.4518\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40560.j have rank \(0\).

Complex multiplication

The elliptic curves in class 40560.j do not have complex multiplication.

Modular form 40560.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - 6 q^{11} + q^{15} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.