Properties

Label 48510x
Number of curves 4
Conductor 48510
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48510.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48510x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48510.q3 48510x1 [1, -1, 0, -220950, -34655580] [2] 589824 \(\Gamma_0(N)\)-optimal
48510.q2 48510x2 [1, -1, 0, -935370, 313838496] [2, 2] 1179648  
48510.q4 48510x3 [1, -1, 0, 1247580, 1559429766] [2] 2359296  
48510.q1 48510x4 [1, -1, 0, -14549040, 21363295050] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 48510x have rank \(0\).

Modular form 48510.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} - 2q^{13} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.