Properties

Label 214795.b
Number of curves $1$
Conductor $214795$
CM no
Rank $1$

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

Elliptic curves in class 214795.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214795.b1 214795a1 \([0, 1, 1, -120, -8106]\) \(-4096/595\) \(-27992299195\) \([]\) \(199584\) \(0.68400\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 214795.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 214795.b do not have complex multiplication.

Modular form 214795.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 4 q^{6} + q^{7} + q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} + q^{13} - 2 q^{14} - 2 q^{15} - 4 q^{16} + q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display