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Properties

Label 5610.r
Number of curves $2$
Conductor $5610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.r1 5610q1 \([1, 0, 1, -103, 398]\) \(-119168121961/2524500\) \(-2524500\) \([3]\) \(1440\) \(0.018888\) \(\Gamma_0(N)\)-optimal
5610.r2 5610q2 \([1, 0, 1, 422, 1868]\) \(8339492177639/6277634880\) \(-6277634880\) \([]\) \(4320\) \(0.56819\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.r have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.r do not have complex multiplication.

Modular form 5610.2.a.r

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.