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Properties

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

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 476850eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.eu1 476850eu1 \([1, 0, 1, -1430701, 658530548]\) \(858729462625/38148\) \(14387499722062500\) \([2]\) \(10616832\) \(2.1777\) \(\Gamma_0(N)\)-optimal
476850.eu2 476850eu2 \([1, 0, 1, -1358451, 728035048]\) \(-735091890625/181908738\) \(-68606792424655031250\) \([2]\) \(21233664\) \(2.5243\)  

Rank

sage: E.rank()
 

The elliptic curves in class 476850eu have rank \(2\).

Complex multiplication

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

Modular form 476850.2.a.eu

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