Properties

Label 6720bb
Number of curves $4$
Conductor $6720$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 6720bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.by3 6720bb1 \([0, 1, 0, -1265, -17745]\) \(13674725584/945\) \(15482880\) \([2]\) \(3072\) \(0.43333\) \(\Gamma_0(N)\)-optimal
6720.by2 6720bb2 \([0, 1, 0, -1345, -15457]\) \(4108974916/893025\) \(58525286400\) \([2, 2]\) \(6144\) \(0.77990\)  
6720.by1 6720bb3 \([0, 1, 0, -6945, 207423]\) \(282678688658/18600435\) \(2437996216320\) \([4]\) \(12288\) \(1.1265\)  
6720.by4 6720bb4 \([0, 1, 0, 2975, -90625]\) \(22208984782/40516875\) \(-5310627840000\) \([2]\) \(12288\) \(1.1265\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6720bb have rank \(1\).

Complex multiplication

The elliptic curves in class 6720bb do not have complex multiplication.

Modular form 6720.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} - 4 q^{11} + 2 q^{13} + q^{15} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.