Properties

Label 405.a
Number of curves $1$
Conductor $405$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405.a1 405f1 \([0, 0, 1, -3, -2]\) \(36864/5\) \(405\) \([]\) \(24\) \(-0.77250\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405.a1 has rank \(1\).

Complex multiplication

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

Modular form 405.2.a.a

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