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Properties

Label 413559k
Number of curves $1$
Conductor $413559$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, -1, 1, -8750, -629612]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 413559k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413559k do not have complex multiplication.

Modular form 413559.2.a.k

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

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

Elliptic curves in class 413559k

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413559.k1 413559k1 \([1, -1, 1, -8750, -629612]\) \(-85117875/148877\) \(-129571108684047\) \([]\) \(895104\) \(1.3984\) \(\Gamma_0(N)\)-optimal