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Properties

Label 476850p
Number of curves $2$
Conductor $476850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 476850p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.p2 476850p1 \([1, 1, 0, 6589050, 998356500]\) \(3355354844375/1987172352\) \(-18736527250504800000000\) \([]\) \(41057280\) \(2.9631\) \(\Gamma_0(N)\)-optimal
476850.p1 476850p2 \([1, 1, 0, -82820325, -320535637875]\) \(-6663170841705625/850403524608\) \(-8018231934792499200000000\) \([]\) \(123171840\) \(3.5124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 476850p have rank \(0\).

Complex multiplication

The elliptic curves in class 476850p do not have complex multiplication.

Modular form 476850.2.a.p

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