Properties

Label 16245.b
Number of curves $1$
Conductor $16245$
CM no
Rank $1$

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

Elliptic curves in class 16245.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.b1 16245i1 \([0, 0, 1, -20577, 32580]\) \(77824/45\) \(557145785560005\) \([]\) \(109440\) \(1.5190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16245.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 16245.b do not have complex multiplication.

Modular form 16245.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + q^{5} - 2 q^{7} - 2 q^{10} + 3 q^{11} + 6 q^{13} + 4 q^{14} - 4 q^{16} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display