↑

Properties

Label 430950bb
Number of curves $2$
Conductor $430950$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 430950bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.bb2 430950bb1 \([1, 1, 0, -60505, 4479415]\) \(203005872265/44836038\) \(5410374793568550\) \([]\) \(2612736\) \(1.7323\) \(\Gamma_0(N)\)-optimal
430950.bb1 430950bb2 \([1, 1, 0, -1568830, -756621380]\) \(3538764637823065/1969338072\) \(237640468249306200\) \([]\) \(7838208\) \(2.2816\)  

Rank

sage: E.rank()
 

The elliptic curves in class 430950bb have rank \(1\).

Complex multiplication

The elliptic curves in class 430950bb do not have complex multiplication.

Modular form 430950.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} + q^{14} + q^{16} - q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.