Properties

Label 2023.a
Number of curves $1$
Conductor $2023$
CM no
Rank $2$

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

Elliptic curves in class 2023.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2023.a1 2023b1 \([1, -1, 1, -12, 0]\) \(610929/343\) \(99127\) \([]\) \(432\) \(-0.35117\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2023.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 2023.a do not have complex multiplication.

Modular form 2023.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3q^{3} - q^{4} - 4q^{5} + 3q^{6} + q^{7} + 3q^{8} + 6q^{9} + 4q^{10} + 3q^{12} - 2q^{13} - q^{14} + 12q^{15} - q^{16} - 6q^{18} - 7q^{19} + O(q^{20})\)  Toggle raw display