Properties

Label 257400a
Number of curves $1$
Conductor $257400$
CM no
Rank $2$

Related objects

Downloads

Learn more

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

Elliptic curves in class 257400a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257400.a1 257400a1 \([0, 0, 0, 2625, 31475]\) \(274400000/217503\) \(-1585596870000\) \([]\) \(516096\) \(1.0289\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257400a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 257400a do not have complex multiplication.

Modular form 257400.2.a.a

sage: E.q_eigenform(10)
 
\(q - 5 q^{7} - q^{11} + q^{13} - 4 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display