Properties

Label 388416e
Number of curves $1$
Conductor $388416$
CM no
Rank $1$

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

Elliptic curves in class 388416e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.e1 388416e1 \([0, -1, 0, 147583, -576159]\) \(449455096/260253\) \(-205844471642750976\) \([]\) \(3612672\) \(2.0116\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 388416e do not have complex multiplication.

Modular form 388416.2.a.e

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