Properties

Label 219584.e
Number of curves $1$
Conductor $219584$
CM no
Rank $0$

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

Elliptic curves in class 219584.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
219584.e1 219584b1 \([0, 0, 0, -316, -2192]\) \(-212992848/3431\) \(-56213504\) \([]\) \(225280\) \(0.28763\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 219584.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 219584.e do not have complex multiplication.

Modular form 219584.2.a.e

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 3 q^{5} + 4 q^{7} + 6 q^{9} - 4 q^{11} + 5 q^{13} - 9 q^{15} - 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display