Properties

Label 4056.f
Number of curves $2$
Conductor $4056$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 4056.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4056.f1 4056k1 \([0, -1, 0, -563, -2172]\) \(256000/117\) \(9035786448\) \([2]\) \(2688\) \(0.60530\) \(\Gamma_0(N)\)-optimal
4056.f2 4056k2 \([0, -1, 0, 1972, -18396]\) \(686000/507\) \(-626481193728\) \([2]\) \(5376\) \(0.95187\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4056.f have rank \(0\).

Complex multiplication

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

Modular form 4056.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} + 2 q^{11} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.