Properties

Label 67270bl
Number of curves $1$
Conductor $67270$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 67270bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.w1 67270bl1 \([1, -1, 1, -2187432, 561639531]\) \(38854571866060040271/17920000000000000\) \(533854720000000000000\) \([]\) \(7128576\) \(2.6719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270bl1 has rank \(2\).

Complex multiplication

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

Modular form 67270.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} + 6 q^{9} + q^{10} - 5 q^{11} - 3 q^{12} - q^{13} - q^{14} - 3 q^{15} + q^{16} + 6 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display