Properties

Label 309168.bb
Number of curves $2$
Conductor $309168$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 309168.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.bb1 309168bb2 \([0, 0, 0, -364183995, -1437542192662]\) \(1788952473315990499029625/736296634487918297088\) \(2198569969834772228412014592\) \([]\) \(116951040\) \(3.9439\)  
309168.bb2 309168bb1 \([0, 0, 0, -168675915, 843121947386]\) \(177744208950637895247625/17681950027579392\) \(52798019871151623241728\) \([]\) \(38983680\) \(3.3946\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 309168.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 309168.bb do not have complex multiplication.

Modular form 309168.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{7} - 3 q^{11} + 2 q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.