Properties

Label 13005j
Number of curves $1$
Conductor $13005$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 13005j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.d1 13005j1 \([1, -1, 1, 22, -34]\) \(5831/5\) \(-1053405\) \([]\) \(2160\) \(-0.15679\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 13005j do not have complex multiplication.

Modular form 13005.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 5 q^{7} + 3 q^{8} + q^{10} + 2 q^{11} + 2 q^{13} - 5 q^{14} - q^{16} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display