Properties

Label 207368.g
Number of curves $2$
Conductor $207368$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 207368.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207368.g1 207368q2 \([0, 1, 0, -12658088, 17328498592]\) \(12576878500/1127\) \(20099216529091632128\) \([2]\) \(8110080\) \(2.7439\)  
207368.g2 207368q1 \([0, 1, 0, -734428, 311051040]\) \(-9826000/3703\) \(-16510070720325269248\) \([2]\) \(4055040\) \(2.3974\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 207368.g have rank \(1\).

Complex multiplication

The elliptic curves in class 207368.g do not have complex multiplication.

Modular form 207368.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{9} - 4q^{11} - 6q^{13} + O(q^{20})\)  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.