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Properties

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

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Show commands: SageMath
E = EllipticCurve("fw1")
 
E.isogeny_class()
 

Elliptic curves in class 476850.fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.fw1 476850fw2 \([1, 1, 1, -343453810038, -77473187076227469]\) \(2418067440128989194388361/8359273562112\) \(15489195324818361163776000000\) \([2]\) \(3556245504\) \(5.0529\)  
476850.fw2 476850fw1 \([1, 1, 1, -21475442038, -1209390831747469]\) \(591139158854005457801/1097587482427392\) \(2033758887668011254153216000000\) \([2]\) \(1778122752\) \(4.7064\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 476850.fw1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 476850.2.a.fw

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