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Properties

Label 462722l
Number of curves $2$
Conductor $462722$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462722l have rank \(0\).

Complex multiplication

The elliptic curves in class 462722l do not have complex multiplication.

Modular form 462722.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - 3 q^{9} - q^{10} - 4 q^{11} - 4 q^{14} + q^{16} - 3 q^{17} - 3 q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 462722l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462722.l2 462722l1 \([1, -1, 1, 1112, 61455]\) \(351/4\) \(-1734431052484\) \([]\) \(619920\) \(1.0294\) \(\Gamma_0(N)\)-optimal
462722.l1 462722l2 \([1, -1, 1, -532798, -149611315]\) \(-38575685889/16384\) \(-7104229590974464\) \([]\) \(4339440\) \(2.0024\)