Properties

Label 250173.i
Number of curves $1$
Conductor $250173$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 250173.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.i1 250173i1 \([1, -1, 1, 6772, -110140]\) \(6869835701/4991679\) \(-24959448244269\) \([]\) \(460800\) \(1.2590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.i1 has rank \(2\).

Complex multiplication

The elliptic curves in class 250173.i do not have complex multiplication.

Modular form 250173.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + q^{7} + 3 q^{8} + q^{10} + q^{11} - 4 q^{13} - q^{14} - q^{16} + O(q^{20})\) Copy content Toggle raw display