Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 250173.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.k1 250173k1 \([1, -1, 1, -9109181, 11340411994]\) \(-13160971881/1127357\) \(-7160365095635904347349\) \([]\) \(16780800\) \(2.9382\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.k1 has rank \(1\).

Complex multiplication

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

Modular form 250173.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 3 q^{8} - 3 q^{10} - q^{11} + 2 q^{13} + q^{14} - q^{16} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display