Properties

Label 27808.a
Number of curves $1$
Conductor $27808$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 27808.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27808.a1 27808a1 \([0, 0, 0, -364, 2656]\) \(1302170688/9559\) \(39153664\) \([]\) \(34560\) \(0.28796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27808.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 27808.a do not have complex multiplication.

Modular form 27808.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 3 q^{5} - 5 q^{7} + 6 q^{9} - q^{11} - 7 q^{13} + 9 q^{15} - 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display