↑

Properties

Label 271062.b
Number of curves $2$
Conductor $271062$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 271062.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271062.b1 271062b2 \([1, -1, 0, -1416006, -648202604]\) \(-8503279704467029/46382688\) \(-1712728853247456\) \([]\) \(4032000\) \(2.1168\)  
271062.b2 271062b1 \([1, -1, 0, 7569, -218237]\) \(1298596571/1299078\) \(-47969802293886\) \([]\) \(806400\) \(1.3121\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 271062.b have rank \(0\).

Complex multiplication

The elliptic curves in class 271062.b do not have complex multiplication.

Modular form 271062.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - 2 q^{7} - q^{8} + 3 q^{10} + q^{11} + 4 q^{13} + 2 q^{14} + q^{16} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.