Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 86394.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86394.r1 86394e1 \([1, 1, 0, -1695333, 1004093325]\) \(-2513898149714809/579901980672\) \(-124307139666533548032\) \([]\) \(7037184\) \(2.5754\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 86394.r1 has rank \(1\).

Complex multiplication

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

Modular form 86394.2.a.r

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