Properties

Label 33489.e
Number of curves $1$
Conductor $33489$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 33489.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33489.e1 33489f1 \([1, -1, 1, -67676, -7140076]\) \(-912673/61\) \(-2291059527459309\) \([]\) \(178560\) \(1.6993\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33489.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 33489.e do not have complex multiplication.

Modular form 33489.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 3 q^{8} - 3 q^{10} - 5 q^{11} + q^{13} + q^{14} - q^{16} + 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display