Properties

Label 272976e
Number of curves $1$
Conductor $272976$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 272976e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272976.e1 272976e1 \([0, -1, 0, -23877, 546669]\) \(207474688/102789\) \(745869244944384\) \([]\) \(1332800\) \(1.5468\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272976e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272976e do not have complex multiplication.

Modular form 272976.2.a.e

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