Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29645.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.f1 29645i1 \([1, -1, 1, -573, -11294]\) \(-1459161/3125\) \(-44486028125\) \([]\) \(39600\) \(0.73212\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29645.f1 has rank \(1\).

Complex multiplication

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

Modular form 29645.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3q^{3} - q^{4} - q^{5} - 3q^{6} + 3q^{8} + 6q^{9} + q^{10} - 3q^{12} - 4q^{13} - 3q^{15} - q^{16} - 6q^{18} - 4q^{19} + O(q^{20})\)  Toggle raw display