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Properties

Label 2790n
Number of curves $2$
Conductor $2790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 2790n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.s1 2790n1 \([1, -1, 1, -1067393, 248622481]\) \(6832900384593441003/2600468480000000\) \(51185021091840000000\) \([2]\) \(100800\) \(2.4812\) \(\Gamma_0(N)\)-optimal
2790.s2 2790n2 \([1, -1, 1, 3356287, 1775676817]\) \(212427047662836354837/192200000000000000\) \(-3783072600000000000000\) \([2]\) \(201600\) \(2.8278\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2790n have rank \(0\).

Complex multiplication

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

Modular form 2790.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.