Properties

Label 3822.be
Number of curves $1$
Conductor $3822$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.be1 3822ba1 \([1, 0, 0, -69336, 96787872]\) \(-6394640503489/698390001504\) \(-4026079379060260704\) \([]\) \(85680\) \(2.2495\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.be1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3822.be do not have complex multiplication.

Modular form 3822.2.a.be

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