Properties

Label 177600hb
Number of curves $1$
Conductor $177600$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hb1")
 
E.isogeny_class()
 

Elliptic curves in class 177600hb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177600.d1 177600hb1 \([0, -1, 0, -53, -723]\) \(-8192/111\) \(-227328000\) \([]\) \(70656\) \(0.28509\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177600hb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177600hb do not have complex multiplication.

Modular form 177600.2.a.hb

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - 6 q^{11} + q^{13} - 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display