Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 250173.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.f1 250173f1 \([1, -1, 1, -2804, 61924]\) \(-13160971881/1127357\) \(-208778624901\) \([]\) \(294400\) \(0.91670\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.f1 has rank \(2\).

Complex multiplication

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

Modular form 250173.2.a.f

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