Properties

Label 6034.b
Number of curves $1$
Conductor $6034$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 6034.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6034.b1 6034d1 \([1, -1, 0, 35, 49]\) \(4665834711/4139324\) \(-4139324\) \([]\) \(2304\) \(-0.042897\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6034.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6034.b do not have complex multiplication.

Modular form 6034.2.a.b

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