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Properties

Label 2070.d
Number of curves $2$
Conductor $2070$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2070.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.d1 2070d2 \([1, -1, 0, -39, 95]\) \(246491883/26450\) \(714150\) \([2]\) \(384\) \(-0.14257\)  
2070.d2 2070d1 \([1, -1, 0, -9, -7]\) \(3176523/460\) \(12420\) \([2]\) \(192\) \(-0.48915\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2070.d have rank \(1\).

Complex multiplication

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

Modular form 2070.2.a.d

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