Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2070.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.g1 2070g2 \([1, -1, 0, -7074, 160380]\) \(53706380371489/16171875000\) \(11789296875000\) \([2]\) \(3840\) \(1.2134\)  
2070.g2 2070g1 \([1, -1, 0, 1206, 16308]\) \(265971760991/317400000\) \(-231384600000\) \([2]\) \(1920\) \(0.86683\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2070.2.a.g

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