Properties

Label 309168.w
Number of curves $1$
Conductor $309168$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 309168.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.w1 309168w1 \([0, 0, 0, -363, 3114]\) \(-191328588/40793\) \(-1127844864\) \([]\) \(84992\) \(0.45829\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 309168.w1 has rank \(2\).

Complex multiplication

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

Modular form 309168.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3 q^{7} + q^{13} - 3 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display