Properties

Label 4056.a
Number of curves $2$
Conductor $4056$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4056.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4056.a1 4056d1 \([0, -1, 0, -110075, 13242696]\) \(1909913257984/129730653\) \(10018961335620432\) \([2]\) \(40320\) \(1.8189\) \(\Gamma_0(N)\)-optimal
4056.a2 4056d2 \([0, -1, 0, 95260, 56773716]\) \(77366117936/1172914587\) \(-1449327279299298048\) \([2]\) \(80640\) \(2.1654\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4056.a have rank \(1\).

Complex multiplication

The elliptic curves in class 4056.a do not have complex multiplication.

Modular form 4056.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + q^{9} + 2 q^{11} + 4 q^{15} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.