Properties

Label 1323.b
Number of curves $1$
Conductor $1323$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 1323.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1323.b1 1323r1 \([0, 0, 1, -147, -86]\) \(12288/7\) \(200120949\) \([]\) \(576\) \(0.28269\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1323.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1323.b do not have complex multiplication.

Modular form 1323.2.a.b

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