Properties

Label 10192.y
Number of curves $1$
Conductor $10192$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 10192.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10192.y1 10192v1 \([0, 1, 0, -3613080, 2646827924]\) \(-10824513276632329/21926008832\) \(-10565931061559164928\) \([]\) \(354816\) \(2.5373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10192.y1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10192.y do not have complex multiplication.

Modular form 10192.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - 2 q^{9} + q^{11} - q^{13} - 4 q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display