Properties

Label 705600.bkd
Number of curves $2$
Conductor $705600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bkd1")
 
E.isogeny_class()
 

Elliptic curves in class 705600.bkd

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bkd1 \([0, 0, 0, -266700, -37926000]\) \(55306341/15625\) \(592704000000000000\) \([2]\) \(9437184\) \(2.1172\)
705600.bkd2 \([0, 0, 0, -98700, 11466000]\) \(2803221/125\) \(4741632000000000\) \([2]\) \(4718592\) \(1.7706\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.bkd have rank \(1\).

Complex multiplication

The elliptic curves in class 705600.bkd do not have complex multiplication.

Modular form 705600.2.a.bkd

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} - 6 q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.