Properties

Label 254320.r
Number of curves $1$
Conductor $254320$
CM no
Rank $1$

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

Elliptic curves in class 254320.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254320.r1 254320r1 \([0, -1, 0, -445445, 135613357]\) \(-1183744/275\) \(-2270815529465753600\) \([]\) \(2741760\) \(2.2417\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 254320.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 254320.r do not have complex multiplication.

Modular form 254320.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2 q^{9} - q^{11} - q^{15} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display