Properties

Label 87120.ew
Number of curves $2$
Conductor $87120$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ew1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ew1 87120bp2 \([0, 0, 0, -1947, 32186]\) \(821516/25\) \(24839654400\) \([2]\) \(55296\) \(0.77072\)  
87120.ew2 87120bp1 \([0, 0, 0, 33, 1694]\) \(16/5\) \(-1241982720\) \([2]\) \(27648\) \(0.42414\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.ew have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.ew do not have complex multiplication.

Modular form 87120.2.a.ew

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{13} + 6q^{17} + O(q^{20})\)  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.