Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 28611q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28611.l1 28611q1 \([0, 0, 1, -9699996, 11628030672]\) \(-5736108018368512/11042163\) \(-194301078093553563\) \([]\) \(737280\) \(2.5712\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28611q1 has rank \(1\).

Complex multiplication

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

Modular form 28611.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 2 q^{5} + 3 q^{7} + q^{11} + 2 q^{13} + 4 q^{16} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display