Properties

Label 13872.u
Number of curves $1$
Conductor $13872$
CM no
Rank $2$

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

Elliptic curves in class 13872.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13872.u1 13872p1 \([0, 1, 0, 40, 3684]\) \(23324/19683\) \(-5824908288\) \([]\) \(15552\) \(0.55281\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13872.u1 has rank \(2\).

Complex multiplication

The elliptic curves in class 13872.u do not have complex multiplication.

Modular form 13872.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - 5 q^{7} + q^{9} - q^{13} - 4 q^{15} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display