Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29645.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.p1 29645j1 \([0, 0, 1, -41503, 5592529]\) \(-110592/125\) \(-8936109546315875\) \([]\) \(480480\) \(1.7551\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29645.p1 has rank \(1\).

Complex multiplication

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

Modular form 29645.2.a.p

sage: E.q_eigenform(10)
 
\(q + 2q^{2} + 3q^{3} + 2q^{4} - q^{5} + 6q^{6} + 6q^{9} - 2q^{10} + 6q^{12} - 3q^{13} - 3q^{15} - 4q^{16} + 3q^{17} + 12q^{18} - 6q^{19} + O(q^{20})\)  Toggle raw display