Properties

Label 178752.ha
Number of curves $1$
Conductor $178752$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ha1")
 
E.isogeny_class()
 

Elliptic curves in class 178752.ha

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
178752.ha1 178752gh1 \([0, 1, 0, 4179999, -2635353729]\) \(628805222251722551/597713542447104\) \(-7677663924691427917824\) \([]\) \(10838016\) \(2.8865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 178752.ha1 has rank \(1\).

Complex multiplication

The elliptic curves in class 178752.ha do not have complex multiplication.

Modular form 178752.2.a.ha

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - 3 q^{11} - 4 q^{13} - q^{15} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display