Properties

Label 465690.p
Number of curves $2$
Conductor $465690$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 465690.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
465690.p1 465690p1 \([1, 0, 1, -9615604, 11512499906]\) \(-5789279907940249/21466890000\) \(-364584279609212490000\) \([3]\) \(45702144\) \(2.8056\) \(\Gamma_0(N)\)-optimal
465690.p2 465690p2 \([1, 0, 1, 21352781, 60244350542]\) \(63395476613331191/129000000000000\) \(-2190879632289000000000000\) \([]\) \(137106432\) \(3.3549\)  

Rank

sage: E.rank()
 

The elliptic curves in class 465690.p have rank \(1\).

Complex multiplication

The elliptic curves in class 465690.p do not have complex multiplication.

Modular form 465690.2.a.p

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.