Properties

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

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

Elliptic curves in class 13005.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.e1 13005q1 \([1, -1, 1, 6448, -139944]\) \(5831/5\) \(-25426635872445\) \([]\) \(36720\) \(1.2598\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005.e1 has rank \(0\).

Complex multiplication

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

Modular form 13005.2.a.e

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