Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 250173.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.s1 250173s1 \([0, 0, 1, -3078, 56045]\) \(23887872/3773\) \(509376494781\) \([]\) \(207360\) \(0.96913\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.s1 has rank \(2\).

Complex multiplication

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

Modular form 250173.2.a.s

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} + q^{7} - q^{11} - 4 q^{13} + 4 q^{16} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display