Properties

Label 18515.u
Number of curves $1$
Conductor $18515$
CM no
Rank $0$

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

Elliptic curves in class 18515.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.u1 18515u1 \([0, 0, 1, -6877, -599225]\) \(-242970624/907235\) \(-134303339756915\) \([]\) \(190080\) \(1.3966\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18515.u1 has rank \(0\).

Complex multiplication

The elliptic curves in class 18515.u do not have complex multiplication.

Modular form 18515.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 3 q^{3} + 2 q^{4} + q^{5} + 6 q^{6} + q^{7} + 6 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} + 7 q^{13} + 2 q^{14} + 3 q^{15} - 4 q^{16} - 3 q^{17} + 12 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display