Properties

Label 5070.n
Number of curves $2$
Conductor $5070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5070.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.n1 5070m2 \([1, 1, 1, -144076, -21109171]\) \(68523370149961/243360\) \(1174652238240\) \([2]\) \(26880\) \(1.5343\)  
5070.n2 5070m1 \([1, 1, 1, -8876, -342451]\) \(-16022066761/998400\) \(-4819086105600\) \([2]\) \(13440\) \(1.1877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5070.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + 2q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.