Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 272734.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.l1 272734l1 \([1, 1, 0, -27075325, -3224725027]\) \(25286724761962890625/14582131947204448\) \(1265823676471551496063072\) \([]\) \(39744000\) \(3.3144\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734.l1 has rank \(1\).

Complex multiplication

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

Modular form 272734.2.a.l

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