Properties

Label 459.c
Number of curves $1$
Conductor $459$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 459.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459.c1 459h1 \([1, -1, 1, -2, 28]\) \(-27/17\) \(-334611\) \([]\) \(36\) \(-0.26087\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 459.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 459.c do not have complex multiplication.

Modular form 459.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 3 q^{8} - q^{10} - 5 q^{13} + 2 q^{14} - q^{16} + q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display