Properties

Label 50820q
Number of curves $2$
Conductor $50820$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 50820q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.t2 50820q1 \([0, 1, 0, -9960881, 16607633700]\) \(-3856034557002072064/1973796785296875\) \(-55947222508117074750000\) \([2]\) \(4838400\) \(3.0696\) \(\Gamma_0(N)\)-optimal
50820.t1 50820q2 \([0, 1, 0, -175352756, 893581511700]\) \(1314817350433665559504/190690249278375\) \(86481768627672907104000\) \([2]\) \(9676800\) \(3.4161\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50820q have rank \(1\).

Complex multiplication

The elliptic curves in class 50820q do not have complex multiplication.

Modular form 50820.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - q^{15} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.