Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 13005.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.b1 13005a1 \([1, -1, 1, 610747, 124217912]\) \(462866157/390625\) \(-21262435668798046875\) \([]\) \(274176\) \(2.3963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005.b1 has rank \(1\).

Complex multiplication

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

Modular form 13005.2.a.b

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