Properties

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

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Show commands: SageMath
E = EllipticCurve("kl1")
 
E.isogeny_class()
 

Elliptic curves in class 476850kl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.kl2 476850kl1 \([1, 0, 0, -74309488, -246165745408]\) \(591139158854005457801/1097587482427392\) \(84256989080715264000000\) \([2]\) \(104595456\) \(3.2898\) \(\Gamma_0(N)\)-optimal
476850.kl1 476850kl2 \([1, 0, 0, -1188421488, -15769088241408]\) \(2418067440128989194388361/8359273562112\) \(641704859541504000000\) \([2]\) \(209190912\) \(3.6363\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 476850.2.a.kl

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 Cremona 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 Cremona labels.