Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2070.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.c1 2070e2 \([1, -1, 0, -35325, 2564325]\) \(6687281588245201/165600\) \(120722400\) \([2]\) \(3840\) \(1.0692\)  
2070.c2 2070e1 \([1, -1, 0, -2205, 40581]\) \(-1626794704081/8125440\) \(-5923445760\) \([2]\) \(1920\) \(0.72264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2070.2.a.c

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