Properties

Label 48050.u
Number of curves $4$
Conductor $48050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 48050.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48050.u1 48050v4 \([1, 0, 0, -3015638, 2015446892]\) \(-349938025/8\) \(-69336225078125000\) \([]\) \(918000\) \(2.3449\)  
48050.u2 48050v3 \([1, 0, 0, -12513, 6356267]\) \(-25/2\) \(-17334056269531250\) \([]\) \(306000\) \(1.7956\)  
48050.u3 48050v1 \([1, 0, 0, -2903, -72823]\) \(-121945/32\) \(-710002944800\) \([]\) \(61200\) \(0.99089\) \(\Gamma_0(N)\)-optimal
48050.u4 48050v2 \([1, 0, 0, 21122, 537412]\) \(46969655/32768\) \(-727043015475200\) \([]\) \(183600\) \(1.5402\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48050.u have rank \(1\).

Complex multiplication

The elliptic curves in class 48050.u do not have complex multiplication.

Modular form 48050.2.a.u

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

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.