Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("dt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 388416dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.dt1 388416dt1 \([0, -1, 0, 116031, 6462657]\) \(2280364702703/1560674304\) \(-118236085972107264\) \([]\) \(4700160\) \(1.9646\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416dt1 has rank \(1\).

Complex multiplication

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

Modular form 388416.2.a.dt

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