Properties

Label 4102.b
Number of curves $1$
Conductor $4102$
CM no
Rank $2$

Related objects

Downloads

Learn more

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

Elliptic curves in class 4102.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4102.b1 4102a1 \([1, 1, 0, 12, 64]\) \(167284151/1607984\) \(-1607984\) \([]\) \(768\) \(-0.12795\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4102.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 4102.b do not have complex multiplication.

Modular form 4102.2.a.b

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