Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 2790.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.i1 2790c1 \([1, -1, 0, -118599, -9168707]\) \(6832900384593441003/2600468480000000\) \(70212648960000000\) \([2]\) \(33600\) \(1.9319\) \(\Gamma_0(N)\)-optimal
2790.i2 2790c2 \([1, -1, 0, 372921, -65890115]\) \(212427047662836354837/192200000000000000\) \(-5189400000000000000\) \([2]\) \(67200\) \(2.2784\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2790.2.a.i

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 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.