Properties

Label 6672b
Number of curves $2$
Conductor $6672$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 6672b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6672.d1 6672b1 \([0, -1, 0, -1248, -16560]\) \(210094874500/3753\) \(3843072\) \([2]\) \(2688\) \(0.39052\) \(\Gamma_0(N)\)-optimal
6672.d2 6672b2 \([0, -1, 0, -1208, -17712]\) \(-95269531250/14085009\) \(-28846098432\) \([2]\) \(5376\) \(0.73709\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6672b have rank \(0\).

Complex multiplication

The elliptic curves in class 6672b do not have complex multiplication.

Modular form 6672.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} + 2 q^{17} + O(q^{20})\) 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.