Properties

Label 5175.u
Number of curves $1$
Conductor $5175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 5175.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5175.u1 5175p1 \([1, -1, 0, -492, -1459]\) \(46305/23\) \(6549609375\) \([]\) \(1920\) \(0.57653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5175.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5175.u do not have complex multiplication.

Modular form 5175.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{7} - 3 q^{8} + q^{11} + q^{13} + q^{14} - q^{16} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display