Properties

Label 38646.e
Number of curves $1$
Conductor $38646$
CM no
Rank $1$

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

Elliptic curves in class 38646.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.e1 38646a1 \([1, -1, 0, -938733, 356038821]\) \(-3388335951737767194891/64702786021471744\) \(-1746975222579737088\) \([]\) \(648000\) \(2.2946\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38646.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 38646.e do not have complex multiplication.

Modular form 38646.2.a.e

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