Properties

Label 189618.c
Number of curves $1$
Conductor $189618$
CM no
Rank $1$

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

Elliptic curves in class 189618.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.c1 189618bk1 \([1, 1, 0, 38022, 2136906]\) \(1259362112399/1131450606\) \(-5461295968096254\) \([]\) \(1225728\) \(1.7071\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 189618.c do not have complex multiplication.

Modular form 189618.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 3q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + 3q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  Toggle raw display