Properties

Label 2790f
Number of curves $2$
Conductor $2790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2790f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.g2 2790f1 \([1, -1, 0, 561, 1773]\) \(722458663317/476656000\) \(-12869712000\) \([3]\) \(2016\) \(0.62865\) \(\Gamma_0(N)\)-optimal
2790.g1 2790f2 \([1, -1, 0, -6414, -230572]\) \(-1482713947827/325058560\) \(-6398127636480\) \([]\) \(6048\) \(1.1780\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2790f have rank \(1\).

Complex multiplication

The elliptic curves in class 2790f do not have complex multiplication.

Modular form 2790.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 3 q^{11} - 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.