Properties

Label 40656i
Number of curves $4$
Conductor $40656$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 40656i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.bi3 40656i1 \([0, -1, 0, -887, -9810]\) \(2725888/21\) \(595244496\) \([2]\) \(23040\) \(0.51276\) \(\Gamma_0(N)\)-optimal
40656.bi2 40656i2 \([0, -1, 0, -1492, 5920]\) \(810448/441\) \(200002150656\) \([2, 2]\) \(46080\) \(0.85933\)  
40656.bi4 40656i3 \([0, -1, 0, 5768, 40768]\) \(11696828/7203\) \(-13066807176192\) \([2]\) \(92160\) \(1.2059\)  
40656.bi1 40656i4 \([0, -1, 0, -18432, 968112]\) \(381775972/567\) \(1028582489088\) \([2]\) \(92160\) \(1.2059\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40656i have rank \(0\).

Complex multiplication

The elliptic curves in class 40656i do not have complex multiplication.

Modular form 40656.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 2 q^{13} - 2 q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.