Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.a1 8470m1 \([1, -1, 0, -1414, -527180]\) \(-1459161/560000\) \(-120040973360000\) \([]\) \(59136\) \(1.3807\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.a1 has rank \(1\).

Complex multiplication

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

Modular form 8470.2.a.a

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