Properties

Label 272734.b
Number of curves $1$
Conductor $272734$
CM no
Rank $2$

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

Elliptic curves in class 272734.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.b1 272734b1 \([1, -1, 0, -5770, 76852]\) \(34965783/16192\) \(9838994689216\) \([]\) \(1382400\) \(1.1877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 272734.b do not have complex multiplication.

Modular form 272734.2.a.b

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