Properties

Label 272734.g
Number of curves $1$
Conductor $272734$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 272734.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.g1 272734g1 \([1, 0, 1, -17591467, -30913572714]\) \(-197294400193/21102592\) \(-64394814130509694763008\) \([]\) \(27574272\) \(3.1151\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734.g1 has rank \(1\).

Complex multiplication

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

Modular form 272734.2.a.g

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