Properties

Label 29645.k
Number of curves $1$
Conductor $29645$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 29645.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.k1 29645k1 \([1, -1, 0, 236, -2535]\) \(2079/5\) \(-3487704605\) \([]\) \(11088\) \(0.51497\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29645.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 29645.k do not have complex multiplication.

Modular form 29645.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{8} - 3 q^{9} + q^{10} - q^{16} - 6 q^{17} - 3 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display