Properties

Label 271332.a
Number of curves $1$
Conductor $271332$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 271332.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271332.a1 271332a1 \([0, 0, 0, -36489, 2682817]\) \(460640464575232/7537\) \(87911568\) \([]\) \(301680\) \(1.0689\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 271332.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 271332.a do not have complex multiplication.

Modular form 271332.2.a.a

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 2 q^{7} - 2 q^{11} - 2 q^{13} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display