Properties

Label 268770cb
Number of curves $1$
Conductor $268770$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 268770cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
268770.cb1 268770cb1 \([1, 0, 0, -6661745, 6651911025]\) \(-1354547383894636849/8173828125000\) \(-197296340361328125000\) \([]\) \(23063040\) \(2.7338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 268770cb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 268770cb do not have complex multiplication.

Modular form 268770.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} + q^{8} + q^{9} + q^{10} - 5 q^{11} + q^{12} - 6 q^{13} - 3 q^{14} + q^{15} + q^{16} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display