Properties

Label 85176.u
Number of curves $1$
Conductor $85176$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 85176.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.u1 85176bb1 \([0, 0, 0, -85683, 12738206]\) \(-114244/49\) \(-29838046294877184\) \([]\) \(599040\) \(1.8688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 85176.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 85176.u do not have complex multiplication.

Modular form 85176.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 2 q^{11} + 3 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display