Properties

Label 12789p
Number of curves $1$
Conductor $12789$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 12789p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12789.o1 12789p1 \([0, 0, 1, -273, 1125]\) \(62992384/21141\) \(755177661\) \([]\) \(8064\) \(0.40601\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12789p1 has rank \(0\).

Complex multiplication

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

Modular form 12789.2.a.p

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{10} - 2 q^{11} - 7 q^{13} - 4 q^{16} + 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display