Properties

Label 301665x
Number of curves $1$
Conductor $301665$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 301665x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.x1 301665x1 \([0, -1, 1, -804414875, 8783188158383]\) \(-11926249134908509075308544/2246680441062421875\) \(-10844297373044067468046875\) \([]\) \(86184000\) \(3.8053\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 301665x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 301665x do not have complex multiplication.

Modular form 301665.2.a.x

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