Properties

Label 2070.n
Number of curves $2$
Conductor $2070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2070.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.n1 2070j2 \([1, -1, 1, -9706583, 11641474927]\) \(5138442430700033888523/413281250000000\) \(8134614843750000000\) \([2]\) \(112896\) \(2.6743\)  
2070.n2 2070j1 \([1, -1, 1, -565463, 207762031]\) \(-1015884369980369163/358196480000000\) \(-7050381315840000000\) \([2]\) \(56448\) \(2.3277\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2070.n have rank \(0\).

Complex multiplication

The elliptic curves in class 2070.n do not have complex multiplication.

Modular form 2070.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.