Properties

Label 66270.i
Number of curves $1$
Conductor $66270$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 66270.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66270.i1 66270j1 \([1, 0, 1, -270649, -362204884]\) \(-203401212841/5139450000\) \(-55399238222629050000\) \([]\) \(2472960\) \(2.4691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66270.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66270.i do not have complex multiplication.

Modular form 66270.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{7} - q^{8} + q^{9} + q^{10} + 6 q^{11} + q^{12} - q^{13} + 3 q^{14} - q^{15} + q^{16} + 3 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display