↑

Properties

Label 10830.bd
Number of curves $2$
Conductor $10830$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 10830.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.bd1 10830bc2 \([1, 0, 0, -584286, -171951084]\) \(468898230633769/5540400\) \(260652999092400\) \([2]\) \(138240\) \(1.9162\)  
10830.bd2 10830bc1 \([1, 0, 0, -35566, -2835580]\) \(-105756712489/12476160\) \(-586951938696960\) \([2]\) \(69120\) \(1.5696\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10830.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 10830.bd do not have complex multiplication.

Modular form 10830.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - 6 q^{11} + q^{12} + 2 q^{14} - q^{15} + q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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 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.