Properties

Label 592.c
Number of curves $1$
Conductor $592$
CM no
Rank $1$

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

Elliptic curves in class 592.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
592.c1 592a1 \([0, 1, 0, -9, -13]\) \(351232/37\) \(9472\) \([]\) \(32\) \(-0.50224\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 592.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 592.c do not have complex multiplication.

Modular form 592.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} - 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} - 4 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display