Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 13005.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.q1 13005k1 \([0, 0, 1, -5763, 24093]\) \(100471803904/56953125\) \(11998941328125\) \([]\) \(48384\) \(1.1996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005.q1 has rank \(0\).

Complex multiplication

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

Modular form 13005.2.a.q

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