Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("48510.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48510bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48510.w3 48510bb1 [1, -1, 0, -24705, 29091901] [2] 663552 \(\Gamma_0(N)\)-optimal
48510.w2 48510bb2 [1, -1, 0, -1577025, 755888125] [2] 1327104  
48510.w4 48510bb3 [1, -1, 0, 222255, -783554675] [2] 1990656  
48510.w1 48510bb4 [1, -1, 0, -11517165, -14614939319] [2] 3981312  

Rank

sage: E.rank()
 

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

Modular form 48510.2.a.w

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.