Properties

Label 8470.g
Number of curves $1$
Conductor $8470$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.g1 8470j1 \([1, 1, 0, 1692, -842288]\) \(2496791/1433600\) \(-307304891801600\) \([]\) \(27456\) \(1.4590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8470.g do not have complex multiplication.

Modular form 8470.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} - 2 q^{9} + q^{10} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} - 4 q^{17} + 2 q^{18} + 3 q^{19} + O(q^{20})\)  Toggle raw display