Properties

Label 309168.z
Number of curves $1$
Conductor $309168$
CM no
Rank $1$

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

Elliptic curves in class 309168.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.z1 309168z1 \([0, 0, 0, -1125435, -365466998]\) \(105591141062347250/22458378326841\) \(33530179174946998272\) \([]\) \(8644608\) \(2.4610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 309168.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 309168.z do not have complex multiplication.

Modular form 309168.2.a.z

sage: E.q_eigenform(10)
 
\(q - 3 q^{7} - 3 q^{11} - 6 q^{13} + q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display