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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 5070.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.l1 5070p1 \([1, 1, 1, -22461, -1257261]\) \(570403428460237/23887872000\) \(52481654784000\) \([2]\) \(25920\) \(1.3974\) \(\Gamma_0(N)\)-optimal
5070.l2 5070p2 \([1, 1, 1, 10819, -4625197]\) \(63745936931123/4251528000000\) \(-9340607016000000\) \([2]\) \(51840\) \(1.7440\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5070.2.a.l

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