Properties

Label 3744737.a
Number of curves $1$
Conductor $3744737$
CM no
Rank $4$

Related objects

Downloads

Learn more

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

Elliptic curves in class 3744737.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
3744737.a1 \([1, 0, 0, -115, 456]\) \(168288035761/3744737\) \(3744737\) \([]\) \(1703040\) \(0.048837\)

Rank

sage: E.rank()
 

The elliptic curve 3744737.a1 has rank \(4\).

Complex multiplication

The elliptic curves in class 3744737.a do not have complex multiplication.

Modular form 3744737.2.a.a

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