Properties

Label 443760.bv
Number of curves $2$
Conductor $443760$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 443760.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.bv1 443760bv2 \([0, 1, 0, -7026816, -6942767436]\) \(1481933914201/53916840\) \(1396031160708485775360\) \([2]\) \(25546752\) \(2.8271\)  
443760.bv2 443760bv1 \([0, 1, 0, -1110016, 301762484]\) \(5841725401/1857600\) \(48097542143272550400\) \([2]\) \(12773376\) \(2.4805\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 443760.bv1.

Rank

sage: E.rank()
 

The elliptic curves in class 443760.bv have rank \(0\).

Complex multiplication

The elliptic curves in class 443760.bv do not have complex multiplication.

Modular form 443760.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2q^{7} + q^{9} + 2q^{11} - 2q^{13} - q^{15} - 4q^{17} - 6q^{19} + O(q^{20})\)  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 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.