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Properties

Label 462550.q
Number of curves $2$
Conductor $462550$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462550.q have rank \(0\).

Complex multiplication

The elliptic curves in class 462550.q do not have complex multiplication.

Modular form 462550.2.a.q

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{7} - q^{8} - 3 q^{9} - q^{11} + 4 q^{13} - 2 q^{14} + q^{16} + 2 q^{17} + 3 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 462550.q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462550.q1 462550q2 \([1, -1, 0, -43567742, 100670296916]\) \(7872285714957/788037184\) \(915513466520250125000000\) \([2]\) \(77414400\) \(3.3341\) \(\Gamma_0(N)\)-optimal*
462550.q2 462550q1 \([1, -1, 0, -9927742, -10308063084]\) \(93144487437/14372864\) \(16697880267112000000000\) \([2]\) \(38707200\) \(2.9876\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 462550.q1.