Properties

Label 40656.i
Number of curves $2$
Conductor $40656$
CM no
Rank $0$
Graph

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

Elliptic curves in class 40656.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.i1 40656bx2 \([0, -1, 0, -5397, -150819]\) \(35084566528/1029\) \(509988864\) \([]\) \(41472\) \(0.77063\)  
40656.i2 40656bx1 \([0, -1, 0, -117, 189]\) \(360448/189\) \(93671424\) \([]\) \(13824\) \(0.22133\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 40656.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.