Properties

Label 338130.q
Number of curves $1$
Conductor $338130$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338130.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.q1 338130q1 \([1, -1, 0, -131561235, -580826748155]\) \(-171352638803089/14236560\) \(-20922896411941261055760\) \([]\) \(50761728\) \(3.3269\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 338130.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 338130.q do not have complex multiplication.

Modular form 338130.2.a.q

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