Properties

Label 121680bv
Number of curves $4$
Conductor $121680$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121680bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121680.fo4 121680bv1 \([0, 0, 0, -30927, 7430254]\) \(-3631696/24375\) \(-21956961068640000\) \([2]\) \(1032192\) \(1.8190\) \(\Gamma_0(N)\)-optimal
121680.fo3 121680bv2 \([0, 0, 0, -791427, 270411154]\) \(15214885924/38025\) \(137011437068313600\) \([2, 2]\) \(2064384\) \(2.1656\)  
121680.fo2 121680bv3 \([0, 0, 0, -1095627, 43417114]\) \(20183398562/11567205\) \(83357758312361994240\) \([2]\) \(4128768\) \(2.5122\)  
121680.fo1 121680bv4 \([0, 0, 0, -12655227, 17328182794]\) \(31103978031362/195\) \(1405245508392960\) \([4]\) \(4128768\) \(2.5122\)  

Rank

sage: E.rank()
 

The elliptic curves in class 121680bv have rank \(1\).

Complex multiplication

The elliptic curves in class 121680bv do not have complex multiplication.

Modular form 121680.2.a.bv

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