Properties

Label 8664.e
Number of curves $1$
Conductor $8664$
CM no
Rank $1$

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

Elliptic curves in class 8664.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8664.e1 8664j1 \([0, -1, 0, 13, -12]\) \(38912/27\) \(-155952\) \([]\) \(864\) \(-0.31500\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8664.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8664.e do not have complex multiplication.

Modular form 8664.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - 3 q^{7} + q^{9} - 5 q^{13} - 2 q^{15} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display