Properties

Label 435344.s
Number of curves $1$
Conductor $435344$
CM no
Rank $1$

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

Elliptic curves in class 435344.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.s1 435344s1 \([0, -1, 0, -185449, -46217419]\) \(-570820369408/418447211\) \(-517059779604402944\) \([]\) \(4730880\) \(2.0984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 435344.s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 435344.s do not have complex multiplication.

Modular form 435344.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3q^{5} - q^{7} - 2q^{9} - 5q^{11} - 3q^{15} - 4q^{17} + 5q^{19} + O(q^{20})\)  Toggle raw display