Properties

Label 379050z
Number of curves $1$
Conductor $379050$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.z1 379050z1 \([1, 1, 0, -305771700, -2058133326000]\) \(-172041783999846385/1179967488\) \(-21684613290748800000000\) \([]\) \(94348800\) \(3.4666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 379050z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 379050z do not have complex multiplication.

Modular form 379050.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 5q^{11} - q^{12} - 4q^{13} + q^{14} + q^{16} + 2q^{17} - q^{18} + O(q^{20})\)  Toggle raw display