Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 28611x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28611.c1 28611x1 \([0, 0, 1, 153, 344]\) \(1880064/1331\) \(-280416411\) \([]\) \(10368\) \(0.30944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28611x1 has rank \(1\).

Complex multiplication

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

Modular form 28611.2.a.x

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + q^{5} + 2 q^{7} - 2 q^{10} + q^{11} - 2 q^{13} - 4 q^{14} - 4 q^{16} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display