↑

Properties

Label 386575b
Number of curves $2$
Conductor $386575$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 386575b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
386575.b2 386575b1 \([1, -1, 1, -2130, -77128]\) \(-658503/1225\) \(-1987237109375\) \([2]\) \(543744\) \(1.0498\) \(\Gamma_0(N)\)-optimal
386575.b1 386575b2 \([1, -1, 1, -43255, -3449378]\) \(5517084663/4375\) \(7097275390625\) \([2]\) \(1087488\) \(1.3963\)  

Rank

sage: E.rank()
 

The elliptic curves in class 386575b have rank \(0\).

Complex multiplication

The elliptic curves in class 386575b do not have complex multiplication.

Modular form 386575.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} - 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + 3 q^{18} - 8 q^{19} + O(q^{20})\) 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.