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Properties

Label 68970bq
Number of curves $2$
Conductor $68970$
CM no
Rank $0$
Graph

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

Elliptic curves in class 68970bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68970.bk2 68970bq1 \([1, 1, 1, -11921, -554641]\) \(-105756712489/12476160\) \(-22102278485760\) \([2]\) \(207360\) \(1.2964\) \(\Gamma_0(N)\)-optimal
68970.bk1 68970bq2 \([1, 1, 1, -195841, -33439537]\) \(468898230633769/5540400\) \(9815156564400\) \([2]\) \(414720\) \(1.6429\)  

Rank

sage: E.rank()
 

The elliptic curves in class 68970bq have rank \(0\).

Complex multiplication

The elliptic curves in class 68970bq do not have complex multiplication.

Modular form 68970.2.a.bq

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - 2 q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.