Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2070.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.q1 2070s2 \([1, -1, 1, -15737, 669849]\) \(591202341974089/79350000000\) \(57846150000000\) \([2]\) \(7168\) \(1.3682\)  
2070.q2 2070s1 \([1, -1, 1, 1543, 54681]\) \(557644990391/2119680000\) \(-1545246720000\) \([2]\) \(3584\) \(1.0216\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2070.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - 2q^{7} + q^{8} + q^{10} - 6q^{11} - 2q^{13} - 2q^{14} + q^{16} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.