Properties

Label 5070.u
Number of curves $4$
Conductor $5070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5070.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.u1 5070w4 \([1, 0, 0, -14623320, 21522489312]\) \(71647584155243142409/10140000\) \(48943843260000\) \([2]\) \(215040\) \(2.4797\)  
5070.u2 5070w3 \([1, 0, 0, -1049240, 230144160]\) \(26465989780414729/10571870144160\) \(51028397958662785440\) \([2]\) \(215040\) \(2.4797\)  
5070.u3 5070w2 \([1, 0, 0, -914040, 336168000]\) \(17496824387403529/6580454400\) \(31762596522009600\) \([2, 2]\) \(107520\) \(2.1332\)  
5070.u4 5070w1 \([1, 0, 0, -48760, 6842432]\) \(-2656166199049/2658140160\) \(-12830334847549440\) \([2]\) \(53760\) \(1.7866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5070.u have rank \(0\).

Complex multiplication

The elliptic curves in class 5070.u do not have complex multiplication.

Modular form 5070.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + q^{12} - 4q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  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.