Properties

Label 462b
Number of curves $4$
Conductor $462$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 462b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.c4 462b1 \([1, 1, 0, -644, -2352]\) \(29609739866953/15259926528\) \(15259926528\) \([2]\) \(480\) \(0.64616\) \(\Gamma_0(N)\)-optimal
462.c2 462b2 \([1, 1, 0, -5764, 164560]\) \(21184262604460873/216872764416\) \(216872764416\) \([2, 2]\) \(960\) \(0.99273\)  
462.c1 462b3 \([1, 1, 0, -92004, 10703088]\) \(86129359107301290313/9166294368\) \(9166294368\) \([2]\) \(1920\) \(1.3393\)  
462.c3 462b4 \([1, 1, 0, -1444, 410800]\) \(-333345918055753/72923718045024\) \(-72923718045024\) \([2]\) \(1920\) \(1.3393\)  

Rank

sage: E.rank()
 

The elliptic curves in class 462b have rank \(0\).

Complex multiplication

The elliptic curves in class 462b do not have complex multiplication.

Modular form 462.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + 2 q^{13} + q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\)  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 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.