Properties

Label 272734s
Number of curves $1$
Conductor $272734$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 272734s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.s1 272734s1 \([1, -1, 0, -197617646, 1069318441428]\) \(-33843179482786377/26543104\) \(-669393406186212606976\) \([]\) \(39536640\) \(3.3029\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272734s do not have complex multiplication.

Modular form 272734.2.a.s

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