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Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 4650.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.u1 4650t2 \([1, 0, 1, -5576, 158798]\) \(9814089221/69192\) \(135140625000\) \([2]\) \(5760\) \(0.96851\)  
4650.u2 4650t1 \([1, 0, 1, -576, -1202]\) \(10793861/5952\) \(11625000000\) \([2]\) \(2880\) \(0.62193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4650.2.a.u

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