Properties

Label 481338bv
Number of curves $2$
Conductor $481338$
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 481338bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.bv1 481338bv1 \([1, -1, 0, -42969240, 92853995328]\) \(6793805286030262681/1048227429629952\) \(1353752149594284531007488\) \([2]\) \(144506880\) \(3.3538\) \(\Gamma_0(N)\)-optimal
481338.bv2 481338bv2 \([1, -1, 0, 74817000, 512290795968]\) \(35862531227445945959/108547797844556928\) \(-140186004021732513509039232\) \([2]\) \(289013760\) \(3.7004\)  

Rank

sage: E.rank()
 

The elliptic curves in class 481338bv have rank \(0\).

Complex multiplication

The elliptic curves in class 481338bv do not have complex multiplication.

Modular form 481338.2.a.bv

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4q^{5} + 2q^{7} - q^{8} - 4q^{10} + q^{13} - 2q^{14} + q^{16} - q^{17} + 4q^{19} + O(q^{20})\)  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 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.