Properties

Label 2070.r
Number of curves $4$
Conductor $2070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2070.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.r1 2070q3 \([1, -1, 1, -95792, -11362309]\) \(133345896593725369/340006815000\) \(247864968135000\) \([2]\) \(15360\) \(1.6384\)  
2070.r2 2070q2 \([1, -1, 1, -8312, -24901]\) \(87109155423289/49979073600\) \(36434744654400\) \([2, 2]\) \(7680\) \(1.2919\)  
2070.r3 2070q1 \([1, -1, 1, -5432, 154811]\) \(24310870577209/114462720\) \(83443322880\) \([4]\) \(3840\) \(0.94530\) \(\Gamma_0(N)\)-optimal
2070.r4 2070q4 \([1, -1, 1, 33088, -223621]\) \(5495662324535111/3207841648920\) \(-2338516562062680\) \([2]\) \(15360\) \(1.6384\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2070.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} - 6q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.