↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 2790.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.m1 2790d1 \([1, -1, 0, -69, -127]\) \(1860867/620\) \(12203460\) \([2]\) \(576\) \(0.062422\) \(\Gamma_0(N)\)-optimal
2790.m2 2790d2 \([1, -1, 0, 201, -1045]\) \(45499293/48050\) \(-945768150\) \([2]\) \(1152\) \(0.40900\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2790.2.a.m

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 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.