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Properties

Label 2110.f
Number of curves $2$
Conductor $2110$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2110.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2110.f1 2110e2 \([1, 1, 1, -4990, -196425]\) \(-13741393887617761/8364544041020\) \(-8364544041020\) \([]\) \(4800\) \(1.1816\)  
2110.f2 2110e1 \([1, 1, 1, -90, 1255]\) \(-80677568161/675200000\) \(-675200000\) \([5]\) \(960\) \(0.37692\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2110.f have rank \(0\).

Complex multiplication

The elliptic curves in class 2110.f do not have complex multiplication.

Modular form 2110.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3 q^{7} + q^{8} - 2 q^{9} + q^{10} - 3 q^{11} - q^{12} + 4 q^{13} + 3 q^{14} - q^{15} + q^{16} + 3 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.