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Properties

Label 4650.r
Number of curves $2$
Conductor $4650$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4650.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.r1 4650r2 \([1, 0, 1, -4026, 22948]\) \(461710681489/252204840\) \(3940700625000\) \([2]\) \(9216\) \(1.1076\)  
4650.r2 4650r1 \([1, 0, 1, 974, 2948]\) \(6549699311/4017600\) \(-62775000000\) \([2]\) \(4608\) \(0.76107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4650.r have rank \(1\).

Complex multiplication

The elliptic curves in class 4650.r do not have complex multiplication.

Modular form 4650.2.a.r

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