Properties

Label 405e
Number of curves $1$
Conductor $405$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405.f1 405e1 \([0, 0, 1, -27, 47]\) \(36864/5\) \(295245\) \([]\) \(72\) \(-0.22319\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 405e do not have complex multiplication.

Modular form 405.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + q^{5} + 2 q^{10} + 5 q^{11} + 4 q^{13} - 4 q^{16} - 4 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display