Properties

Label 73689.h
Number of curves $1$
Conductor $73689$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 73689.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73689.h1 73689e1 \([1, 1, 1, -287559, 59299824]\) \(-1484391946907017/1946200179\) \(-3447812335309419\) \([]\) \(720000\) \(1.8882\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 73689.h1 has rank \(0\).

Complex multiplication

The elliptic curves in class 73689.h do not have complex multiplication.

Modular form 73689.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - q^{7} + 3 q^{8} + q^{9} - 3 q^{10} + q^{12} + 3 q^{13} + q^{14} - 3 q^{15} - q^{16} - q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display