Properties

Label 250173.a
Number of curves $1$
Conductor $250173$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 250173.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.a1 250173a1 \([0, 0, 1, -1411149, -569744550]\) \(9061356040192/1155048741\) \(39614068215730363509\) \([]\) \(10644480\) \(2.4895\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250173.a do not have complex multiplication.

Modular form 250173.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 3 q^{5} + q^{7} + 6 q^{10} + q^{11} - 4 q^{13} - 2 q^{14} - 4 q^{16} + O(q^{20})\) Copy content Toggle raw display