↑

Properties

Label 67270t
Number of curves $2$
Conductor $67270$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 67270t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.u2 67270t1 \([1, 1, 0, -2328042, 752500196]\) \(1702470121/686000\) \(562265004868829486000\) \([]\) \(3481920\) \(2.6795\) \(\Gamma_0(N)\)-optimal
67270.u1 67270t2 \([1, 1, 0, -163944217, 807896001381]\) \(594559172575321/143360\) \(117501911221567631360\) \([]\) \(10445760\) \(3.2288\)  

Rank

sage: E.rank()
 

The elliptic curves in class 67270t have rank \(0\).

Complex multiplication

The elliptic curves in class 67270t do not have complex multiplication.

Modular form 67270.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} + q^{5} - 2 q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{12} + q^{13} - q^{14} + 2 q^{15} + q^{16} - 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.