Properties

Label 270802t
Number of curves $1$
Conductor $270802$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.t1 270802t1 \([1, 0, 0, -162026, -25117468]\) \(-19287858777773741/877581376\) \(-21403332179264\) \([]\) \(1666560\) \(1.6339\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 270802t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 270802t do not have complex multiplication.

Modular form 270802.2.a.t

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