Properties

Label 413712.ey
Number of curves $1$
Conductor $413712$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("ey1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 413712.ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.ey1 413712ey1 \([0, 0, 0, -1370928, -1099027280]\) \(-692224/867\) \(-356894698552186908672\) \([]\) \(21765120\) \(2.6370\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 413712.ey1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413712.ey do not have complex multiplication.

Modular form 413712.2.a.ey

sage: E.q_eigenform(10)
 
\(q + 4q^{5} - 3q^{7} - 4q^{11} - q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display