Properties

Label 242550.kc
Number of curves $1$
Conductor $242550$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("kc1")
 
E.isogeny_class()
 

Elliptic curves in class 242550.kc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242550.kc1 242550kc1 \([1, -1, 1, -299115830, 1991760017797]\) \(-34068278205171/10307264\) \(-895437170473416417000000\) \([]\) \(54190080\) \(3.5736\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 242550.kc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 242550.kc do not have complex multiplication.

Modular form 242550.2.a.kc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - q^{11} + 2 q^{13} + q^{16} - q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display