Properties

Label 1856.b
Number of curves $1$
Conductor $1856$
CM no
Rank $1$

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

Elliptic curves in class 1856.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1856.b1 1856o1 \([0, 0, 0, -76, -368]\) \(-185193/116\) \(-30408704\) \([]\) \(768\) \(0.13749\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1856.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1856.b do not have complex multiplication.

Modular form 1856.2.a.b

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