Properties

Label 270480.a
Number of curves $1$
Conductor $270480$
CM no
Rank $1$

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

Elliptic curves in class 270480.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.a1 270480a1 \([0, -1, 0, -1863976, -864791024]\) \(1238039614322/157190625\) \(90936239999673600000\) \([]\) \(10725120\) \(2.5589\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 270480.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 270480.a do not have complex multiplication.

Modular form 270480.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 6 q^{11} + 3 q^{13} + q^{15} - q^{19} + O(q^{20})\) Copy content Toggle raw display