Properties

Label 272832.s
Number of curves $1$
Conductor $272832$
CM no
Rank $1$

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

Elliptic curves in class 272832.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272832.s1 272832s1 \([0, -1, 0, -18489, -10809567]\) \(-5802287872/416118303\) \(-50130843883158528\) \([]\) \(2177280\) \(1.8842\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272832.s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272832.s do not have complex multiplication.

Modular form 272832.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} - 3 q^{11} + 5 q^{13} + 2 q^{15} + q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display