Properties

Label 123627n
Number of curves $1$
Conductor $123627$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 123627n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123627.n1 123627n1 \([1, 0, 0, -148, 1259]\) \(-177625/243\) \(-490675563\) \([]\) \(46800\) \(0.36014\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123627n1 has rank \(2\).

Complex multiplication

The elliptic curves in class 123627n do not have complex multiplication.

Modular form 123627.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + 3 q^{8} + q^{9} - 6 q^{11} - q^{12} - 3 q^{13} - q^{16} - 4 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display