Properties

Label 20328.bc
Number of curves $2$
Conductor $20328$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 20328.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20328.bc1 20328g2 \([0, 1, 0, -392, 2352]\) \(2450086/441\) \(1202116608\) \([2]\) \(7680\) \(0.46133\)  
20328.bc2 20328g1 \([0, 1, 0, 48, 240]\) \(8788/21\) \(-28621824\) \([2]\) \(3840\) \(0.11475\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20328.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 20328.bc do not have complex multiplication.

Modular form 20328.2.a.bc

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