Properties

Label 123627.u
Number of curves $1$
Conductor $123627$
CM no
Rank $0$

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

Elliptic curves in class 123627.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123627.u1 123627w1 \([1, 0, 1, -44917687232, -3329834430577147]\) \(170295687079857398473/17163597526568829\) \(1010137619486580640597189943315181\) \([]\) \(955468800\) \(5.0691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123627.u1 has rank \(0\).

Complex multiplication

The elliptic curves in class 123627.u do not have complex multiplication.

Modular form 123627.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + 3 q^{5} + q^{6} - 3 q^{8} + q^{9} + 3 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} + 3 q^{15} - q^{16} - q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display