Properties

Label 28611k
Number of curves $1$
Conductor $28611$
CM no
Rank $1$

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

Elliptic curves in class 28611k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28611.n1 28611k1 \([0, 0, 1, -29478, 3779325]\) \(-557056/891\) \(-4531026512469699\) \([]\) \(156672\) \(1.6953\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28611k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 28611k do not have complex multiplication.

Modular form 28611.2.a.k

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