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Properties

Label 462722f
Number of curves $2$
Conductor $462722$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("f1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462722f have rank \(1\).

Complex multiplication

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

Modular form 462722.2.a.f

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 462722f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462722.f2 462722f1 \([1, -1, 0, 187981, 135581161]\) \(351/4\) \(-8371767414009243556\) \([]\) \(8058960\) \(2.3119\) \(\Gamma_0(N)\)-optimal
462722.f1 462722f2 \([1, -1, 0, -90042809, -328966186899]\) \(-38575685889/16384\) \(-34290759327781861605376\) \([]\) \(56412720\) \(3.2849\)