Properties

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

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

Elliptic curves in class 309168.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.q1 309168q1 \([0, 0, 0, -43796091, -112427271254]\) \(-3111302831921821954873/28165508381540352\) \(-84101757379145386426368\) \([]\) \(31104000\) \(3.2218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 309168.q1 has rank \(1\).

Complex multiplication

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

Modular form 309168.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 2 q^{7} + 4 q^{11} - 5 q^{13} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display