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Properties

Label 416025r
Number of curves $1$
Conductor $416025$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 416025r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416025r do not have complex multiplication.

Modular form 416025.2.a.r

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

Elliptic curves in class 416025r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416025.r1 416025r1 \([1, -1, 1, -110255, -12682128]\) \(7037694889/759375\) \(15993398583984375\) \([]\) \(3225600\) \(1.8433\) \(\Gamma_0(N)\)-optimal