Properties

Label 250470.i
Number of curves $1$
Conductor $250470$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 250470.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250470.i1 250470i1 \([1, -1, 0, -587175, -204326875]\) \(-17335770872841/3953125000\) \(-5105334314953125000\) \([]\) \(6635520\) \(2.3096\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250470.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250470.i do not have complex multiplication.

Modular form 250470.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 3 q^{7} - q^{8} + q^{10} + 4 q^{13} + 3 q^{14} + q^{16} - 4 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display