Properties

Label 338437e
Number of curves $1$
Conductor $338437$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 338437e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338437.e1 338437e1 \([0, 0, 1, -3751, -80193]\) \(3294646272/338437\) \(599561790157\) \([]\) \(1635840\) \(0.99548\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 338437e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 338437e do not have complex multiplication.

Modular form 338437.2.a.e

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