Properties

Label 14450e
Number of curves $1$
Conductor $14450$
CM no
Rank $1$

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

Elliptic curves in class 14450e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14450.e1 14450e1 \([1, 1, 0, 11750, 456500]\) \(2336752783/2500000\) \(-191914062500000\) \([]\) \(53760\) \(1.4273\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14450e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 14450e do not have complex multiplication.

Modular form 14450.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} - 2 q^{9} - 6 q^{11} - q^{12} + 5 q^{13} + q^{16} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display