Properties

Label 38601.a
Number of curves $1$
Conductor $38601$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 38601.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38601.a1 38601a1 \([0, 0, 1, 3, 16]\) \(110592/4289\) \(-115803\) \([]\) \(11552\) \(-0.34849\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38601.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 38601.a do not have complex multiplication.

Modular form 38601.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 4 q^{5} - 2 q^{7} + 8 q^{10} - 4 q^{11} - 6 q^{13} + 4 q^{14} - 4 q^{16} - 5 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display