Properties

Label 3721.a
Number of curves $1$
Conductor $3721$
CM no
Rank $1$

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

Elliptic curves in class 3721.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3721.a1 3721a1 \([1, 0, 1, -7520, 264447]\) \(-912673/61\) \(-3142742836021\) \([]\) \(7440\) \(1.1500\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3721.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3721.a do not have complex multiplication.

Modular form 3721.2.a.a

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