↑

Properties

Label 234135.bc
Number of curves $2$
Conductor $234135$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 234135.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234135.bc1 234135bc2 \([1, -1, 0, -10005, 386370]\) \(2315685267/9245\) \(442208199015\) \([2]\) \(368640\) \(1.0914\)  
234135.bc2 234135bc1 \([1, -1, 0, -930, -225]\) \(1860867/1075\) \(51419558025\) \([2]\) \(184320\) \(0.74478\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 234135.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 234135.bc do not have complex multiplication.

Modular form 234135.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} + 4 q^{7} - 3 q^{8} - q^{10} - 2 q^{13} + 4 q^{14} - q^{16} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.