Properties

Label 456.a
Number of curves $1$
Conductor $456$
CM no
Rank $1$

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

Elliptic curves in class 456.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
456.a1 456d1 \([0, -1, 0, 55, 93]\) \(70575104/61731\) \(-15803136\) \([]\) \(96\) \(0.068805\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 456.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 456.a do not have complex multiplication.

Modular form 456.2.a.a

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