Properties

Label 135.b
Number of curves $1$
Conductor $135$
CM no
Rank $0$

Related objects

Downloads

Learn more

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

Elliptic curves in class 135.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
135.b1 135b1 \([0, 0, 1, -27, -115]\) \(-12288/25\) \(-4428675\) \([]\) \(36\) \(-0.035421\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 135.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 135.b do not have complex multiplication.

Modular form 135.2.a.b

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