Properties

Label 19074u
Number of curves $1$
Conductor $19074$
CM no
Rank $1$

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

Elliptic curves in class 19074u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19074.u1 19074u1 \([1, 1, 1, -57, -201]\) \(-70945777/5808\) \(-1678512\) \([]\) \(4608\) \(-0.059588\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19074u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19074u do not have complex multiplication.

Modular form 19074.2.a.u

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