Properties

Label 457056.i
Number of curves $1$
Conductor $457056$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 457056.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457056.i1 457056i1 \([0, 0, 0, -12696, 584016]\) \(-13824\) \(-16371585036288\) \([]\) \(1140480\) \(1.2851\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457056.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457056.i do not have complex multiplication.

Modular form 457056.2.a.i

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