↑

Properties

Label 372645eg
Number of curves $2$
Conductor $372645$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 372645eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372645.eg2 372645eg1 \([1, -1, 0, -510834, 135134663]\) \(2803221/125\) \(657379642893962625\) \([2]\) \(5160960\) \(2.1816\) \(\Gamma_0(N)\)-optimal
372645.eg1 372645eg2 \([1, -1, 0, -1380339, -446216380]\) \(55306341/15625\) \(82172455361745328125\) \([2]\) \(10321920\) \(2.5281\)  

Rank

sage: E.rank()
 

The elliptic curves in class 372645eg have rank \(1\).

Complex multiplication

The elliptic curves in class 372645eg do not have complex multiplication.

Modular form 372645.2.a.eg

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{8} + q^{10} - 2 q^{11} - q^{16} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.