Properties

Label 53040z
Number of curves $2$
Conductor $53040$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 53040z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53040.cu1 53040z1 \([0, 1, 0, -3089195, 2088807468]\) \(203769809659907949070336/2016474841511325\) \(32263597464181200\) \([2]\) \(1013760\) \(2.3277\) \(\Gamma_0(N)\)-optimal
53040.cu2 53040z2 \([0, 1, 0, -3015500, 2193277500]\) \(-11845731628994222232016/1269935194601506875\) \(-325103409817985760000\) \([2]\) \(2027520\) \(2.6743\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53040z have rank \(0\).

Complex multiplication

The elliptic curves in class 53040z do not have complex multiplication.

Modular form 53040.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{11} + q^{13} + q^{15} - q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.