Properties

Label 102850.u
Number of curves $1$
Conductor $102850$
CM no
Rank $1$

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

Elliptic curves in class 102850.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102850.u1 102850r1 \([1, 1, 0, -2047080, 1302594880]\) \(-21420636414894985/4175798730752\) \(-184942054381243596800\) \([]\) \(4423680\) \(2.6122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 102850.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 102850.u do not have complex multiplication.

Modular form 102850.2.a.u

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