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Properties

Label 5070.g
Number of curves $2$
Conductor $5070$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5070.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.g1 5070g2 \([1, 1, 0, -692, 6726]\) \(16718302693/90\) \(197730\) \([2]\) \(1920\) \(0.21068\)  
5070.g2 5070g1 \([1, 1, 0, -42, 96]\) \(-3869893/300\) \(-659100\) \([2]\) \(960\) \(-0.13590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5070.g have rank \(1\).

Complex multiplication

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

Modular form 5070.2.a.g

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