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Properties

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

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

Elliptic curves in class 2070.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.l1 2070l2 \([1, -1, 1, -1883, -30069]\) \(27333463470867/895491200\) \(24178262400\) \([2]\) \(1792\) \(0.76583\)  
2070.l2 2070l1 \([1, -1, 1, 37, -1653]\) \(212776173/43335680\) \(-1170063360\) \([2]\) \(896\) \(0.41926\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2070.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} - 2 q^{11} + 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.