Properties

Label 20286.bc
Number of curves $1$
Conductor $20286$
CM no
Rank $1$

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

Elliptic curves in class 20286.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.bc1 20286z1 \([1, -1, 0, 104382, 22930452]\) \(503009937352889/1201583849472\) \(-300452436808925184\) \([]\) \(299520\) \(2.0376\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20286.bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20286.bc do not have complex multiplication.

Modular form 20286.2.a.bc

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