Properties

Label 32487.a
Number of curves $1$
Conductor $32487$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32487.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.a1 32487i1 \([0, -1, 1, -702, 104852]\) \(-325660672/40000779\) \(-4706051648571\) \([]\) \(105984\) \(1.1111\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32487.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 32487.a do not have complex multiplication.

Modular form 32487.2.a.a

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