Properties

Label 86394.h
Number of curves $1$
Conductor $86394$
CM no
Rank $1$

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

Elliptic curves in class 86394.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86394.h1 86394m1 \([1, 1, 0, -2877261, 2069553501]\) \(-12289104689575417/1529937859968\) \(-327955767662275175808\) \([]\) \(5322240\) \(2.6710\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 86394.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 86394.h do not have complex multiplication.

Modular form 86394.2.a.h

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