Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2790.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.p1 2790t2 \([1, -1, 1, -18113, 333281]\) \(901456690969801/457629750000\) \(333612087750000\) \([2]\) \(15360\) \(1.4792\)  
2790.p2 2790t1 \([1, -1, 1, 4207, 38657]\) \(11298232190519/7472736000\) \(-5447624544000\) \([2]\) \(7680\) \(1.1326\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2790.2.a.p

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