Properties

Label 177870.io
Number of curves $1$
Conductor $177870$
CM no
Rank $0$

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

Elliptic curves in class 177870.io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.io1 177870r1 \([1, 0, 0, -34040630, -25931039100]\) \(3432365662485529/1757812500000\) \(2234063329890820312500000\) \([]\) \(35481600\) \(3.3644\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177870.io1 has rank \(0\).

Complex multiplication

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

Modular form 177870.2.a.io

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