Properties

Label 3168.u
Number of curves $4$
Conductor $3168$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 3168.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3168.u1 3168m2 \([0, 0, 0, -4764, -126560]\) \(4004529472/99\) \(295612416\) \([2]\) \(2048\) \(0.73453\)  
3168.u2 3168m3 \([0, 0, 0, -1299, 16198]\) \(649461896/72171\) \(26937681408\) \([2]\) \(2048\) \(0.73453\)  
3168.u3 3168m1 \([0, 0, 0, -309, -1820]\) \(69934528/9801\) \(457275456\) \([2, 2]\) \(1024\) \(0.38795\) \(\Gamma_0(N)\)-optimal
3168.u4 3168m4 \([0, 0, 0, 501, -9758]\) \(37259704/131769\) \(-49182515712\) \([2]\) \(2048\) \(0.73453\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3168.u have rank \(1\).

Complex multiplication

The elliptic curves in class 3168.u do not have complex multiplication.

Modular form 3168.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.