Properties

Label 300560bq
Number of curves $2$
Conductor $300560$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 300560bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300560.bq2 300560bq1 \([0, -1, 0, -15376931760, -632222462862400]\) \(827813553991775477153/123566310400000000\) \(60020598197883562675404800000000\) \([2]\) \(601620480\) \(4.8221\) \(\Gamma_0(N)\)-optimal
300560.bq1 300560bq2 \([0, -1, 0, -236435205040, -44249141940429888]\) \(3009261308803109129809313/85820312500000000\) \(41686010346225440000000000000000\) \([2]\) \(1203240960\) \(5.1686\)  

Rank

sage: E.rank()
 

The elliptic curves in class 300560bq have rank \(1\).

Complex multiplication

The elliptic curves in class 300560bq do not have complex multiplication.

Modular form 300560.2.a.bq

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + q^{9} - q^{13} + 2 q^{15} + O(q^{20})\) 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.