Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 2790.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.v1 2790x2 \([1, -1, 1, -1966028, -1060550449]\) \(1152829477932246539641/3188367360\) \(2324319805440\) \([2]\) \(33280\) \(2.0310\)  
2790.v2 2790x1 \([1, -1, 1, -122828, -16561969]\) \(-281115640967896441/468084326400\) \(-341233473945600\) \([2]\) \(16640\) \(1.6845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2790.2.a.v

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