Properties

Label 12789.q
Number of curves $1$
Conductor $12789$
CM no
Rank $1$

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

Elliptic curves in class 12789.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12789.q1 12789j1 \([0, 0, 1, -1029, 46219]\) \(-4096/29\) \(-853115605587\) \([]\) \(20160\) \(0.97254\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12789.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12789.q do not have complex multiplication.

Modular form 12789.2.a.q

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 6 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display