Properties

Label 67270.a
Number of curves $1$
Conductor $67270$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 67270.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.a1 67270d1 \([1, -1, 0, -17101360360, 798392935825216]\) \(623225944950388227633972249/50391363524359094272000\) \(44722520618477829332226015232000\) \([]\) \(566092800\) \(4.8162\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270.a1 has rank \(0\).

Complex multiplication

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

Modular form 67270.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} - q^{5} + 3 q^{6} - q^{7} - q^{8} + 6 q^{9} + q^{10} + 5 q^{11} - 3 q^{12} - q^{13} + q^{14} + 3 q^{15} + q^{16} + 4 q^{17} - 6 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display