Properties

Label 5070.v
Number of curves $2$
Conductor $5070$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5070.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.v1 5070u1 \([1, 0, 0, -143400, 20940750]\) \(-2365581049/6750\) \(-930544819980750\) \([]\) \(39312\) \(1.7439\) \(\Gamma_0(N)\)-optimal
5070.v2 5070u2 \([1, 0, 0, 285015, 107394897]\) \(18573478391/46875000\) \(-6462116805421875000\) \([]\) \(117936\) \(2.2932\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5070.v have rank \(0\).

Complex multiplication

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

Modular form 5070.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} + 3q^{11} + q^{12} - 2q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.