Properties

Label 177870io
Number of curves $1$
Conductor $177870$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("io1")
 
E.isogeny_class()
 

Elliptic curves in class 177870io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.s1 177870io1 \([1, 1, 0, -11288, -493632]\) \(-3833145796183/270000000\) \(-11205810000000\) \([]\) \(564480\) \(1.2543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177870io1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177870io do not have complex multiplication.

Modular form 177870.2.a.io

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