Properties

Label 474320.hk
Number of curves $1$
Conductor $474320$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("hk1")
 
E.isogeny_class()
 

Elliptic curves in class 474320.hk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
474320.hk1 474320hk1 \([0, 1, 0, -23812840, 40557550900]\) \(85713473128801/8800000000\) \(153317204200652800000000\) \([]\) \(36495360\) \(3.1844\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 474320.hk1 has rank \(2\).

Complex multiplication

The elliptic curves in class 474320.hk do not have complex multiplication.

Modular form 474320.2.a.hk

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