Properties

Label 162624hp
Number of curves $1$
Conductor $162624$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hp1")
 
E.isogeny_class()
 

Elliptic curves in class 162624hp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.bx1 162624hp1 \([0, -1, 0, -803601, -286913031]\) \(-31636584484096/1331669031\) \(-2415752110312848384\) \([]\) \(2764800\) \(2.2940\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624hp1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162624hp do not have complex multiplication.

Modular form 162624.2.a.hp

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 3 q^{13} + q^{15} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display