↑

Properties

Label 58482.p
Number of curves $2$
Conductor $58482$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 58482.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58482.p1 58482y1 \([1, -1, 1, -2234, -43811]\) \(-35937/4\) \(-137185788996\) \([]\) \(82944\) \(0.87441\) \(\Gamma_0(N)\)-optimal
58482.p2 58482y2 \([1, -1, 1, 14011, 60157]\) \(109503/64\) \(-177792782538816\) \([]\) \(248832\) \(1.4237\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58482.p have rank \(1\).

Complex multiplication

The elliptic curves in class 58482.p do not have complex multiplication.

Modular form 58482.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.