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Properties

Label 177858971.a
Number of curves $1$
Conductor $177858971$
CM no
Rank $5$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 177858971.a1 has rank \(5\).

Complex multiplication

The elliptic curves in class 177858971.a do not have complex multiplication.

Modular form 177858971.2.a.a

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} - 5 q^{13} + 10 q^{14} + 9 q^{15} - 4 q^{16} - 6 q^{17} - 12 q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 177858971.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
177858971.a1 \([0, 0, 1, -679, 6840]\) \(-34620476018688/177858971\) \(-177858971\) \([]\) \(\) \(0.42931\)