Properties

Label 227136.em
Number of curves $1$
Conductor $227136$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 227136.em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227136.em1 227136ef1 \([0, -1, 0, -1281089, 624949857]\) \(-20994006260678308/3063651608241\) \(-33931730733808287744\) \([]\) \(7372800\) \(2.4779\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 227136.em1 has rank \(1\).

Complex multiplication

The elliptic curves in class 227136.em do not have complex multiplication.

Modular form 227136.2.a.em

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} + q^{7} + q^{9} - 3 q^{15} + 7 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display