Properties

Label 57150.q
Number of curves $1$
Conductor $57150$
CM no
Rank $1$

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

Elliptic curves in class 57150.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57150.q1 57150q1 \([1, -1, 0, -342, 756]\) \(243135625/130048\) \(2370124800\) \([]\) \(36000\) \(0.49011\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57150.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 57150.q do not have complex multiplication.

Modular form 57150.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} + 6 q^{11} + q^{13} + q^{16} - 7 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display