Properties

Label 211185bc
Number of curves $1$
Conductor $211185$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 211185bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
211185.bb1 211185bc1 \([0, 0, 1, -1083, -125177]\) \(-4096/195\) \(-6687807213555\) \([]\) \(684288\) \(1.1409\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 211185bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 211185bc do not have complex multiplication.

Modular form 211185.2.a.bc

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