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Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 5070.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.e1 5070e2 \([1, 1, 0, -7777, -239741]\) \(10779215329/1232010\) \(5946676956090\) \([2]\) \(16128\) \(1.1834\)  
5070.e2 5070e1 \([1, 1, 0, 673, -18351]\) \(6967871/35100\) \(-169420995900\) \([2]\) \(8064\) \(0.83686\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5070.2.a.e

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