Properties

Label 457136.a
Number of curves $1$
Conductor $457136$
CM no
Rank $1$

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

Elliptic curves in class 457136.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457136.a1 457136a1 \([0, 1, 0, -69, -589]\) \(-8998912/28571\) \(-117026816\) \([]\) \(169600\) \(0.23465\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457136.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457136.a do not have complex multiplication.

Modular form 457136.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + 4 q^{7} - 2 q^{9} + 6 q^{11} - 2 q^{13} - 2 q^{15} - 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display