Properties

Label 1728.e
Number of curves $1$
Conductor $1728$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 1728.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.e1 1728ba1 \([0, 0, 0, -6, 6]\) \(-13824\) \(-1728\) \([]\) \(96\) \(-0.62918\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1728.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1728.e do not have complex multiplication.

Modular form 1728.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 3 q^{7} + 6 q^{11} + 3 q^{13} - 2 q^{17} - 3 q^{19} + O(q^{20})\)  Toggle raw display