Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 2790o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.w1 2790o1 \([1, -1, 1, -8, 7]\) \(1860867/620\) \(16740\) \([2]\) \(192\) \(-0.48688\) \(\Gamma_0(N)\)-optimal
2790.w2 2790o2 \([1, -1, 1, 22, 31]\) \(45499293/48050\) \(-1297350\) \([2]\) \(384\) \(-0.14031\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2790.2.a.o

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