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Properties

Label 414050.fm
Number of curves $1$
Conductor $414050$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fm1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 414050.fm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 414050.fm do not have complex multiplication.

Modular form 414050.2.a.fm

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

Elliptic curves in class 414050.fm

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414050.fm1 414050fm1 \([1, -1, 1, -231055, -4447803]\) \(590625/338\) \(780679791582031250\) \([]\) \(5080320\) \(2.1230\) \(\Gamma_0(N)\)-optimal