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Properties

Label 476850.l
Number of curves $2$
Conductor $476850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 476850.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.l1 476850l2 \([1, 1, 0, -8006073225, 196542649261125]\) \(150476552140919246594353/42832838728685592576\) \(16154384379367512032954496000000\) \([2]\) \(1196163072\) \(4.6950\) \(\Gamma_0(N)\)-optimal*
476850.l2 476850l1 \([1, 1, 0, -2975161225, -60038893650875]\) \(7722211175253055152433/340131399900069888\) \(128280392721164531662848000000\) \([2]\) \(598081536\) \(4.3484\) \(\Gamma_0(N)\)-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 476850.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 476850.l have rank \(1\).

Complex multiplication

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

Modular form 476850.2.a.l

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.