Properties

Label 45693.a
Number of curves $1$
Conductor $45693$
CM no
Rank $0$

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

Elliptic curves in class 45693.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45693.a1 45693a1 \([0, 0, 1, -63, -169]\) \(37933056/5077\) \(3701133\) \([]\) \(27776\) \(-0.012084\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 45693.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 45693.a do not have complex multiplication.

Modular form 45693.2.a.a

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 4 q^{7} + 8 q^{10} + 6 q^{11} - 4 q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display