Properties

Label 388710v
Number of curves $2$
Conductor $388710$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 388710v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388710.v2 388710v1 \([1, -1, 0, -1240485, -539476075]\) \(-289581579184798874961/5081260310000000\) \(-3704238765990000000\) \([]\) \(12216288\) \(2.3604\) \(\Gamma_0(N)\)-optimal
388710.v1 388710v2 \([1, -1, 0, -11437035, 65138641955]\) \(-226953328047600468451761/2382836194386693393110\) \(-1737087585707899483577190\) \([]\) \(85514016\) \(3.3333\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388710v have rank \(1\).

Complex multiplication

The elliptic curves in class 388710v do not have complex multiplication.

Modular form 388710.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + 2 q^{11} - 7 q^{13} - q^{14} + q^{16} - 4 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.