Properties

Label 115920.bm
Number of curves $2$
Conductor $115920$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bm1 115920dk2 \([0, 0, 0, -33123, 2282978]\) \(1345938541921/24850350\) \(74202747494400\) \([2]\) \(294912\) \(1.4560\)  
115920.bm2 115920dk1 \([0, 0, 0, -3, 103682]\) \(-1/1555260\) \(-4643981475840\) \([2]\) \(147456\) \(1.1094\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.bm have rank \(2\).

Complex multiplication

The elliptic curves in class 115920.bm do not have complex multiplication.

Modular form 115920.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 2q^{11} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.