Properties

Label 575.a
Number of curves $1$
Conductor $575$
CM no
Rank $1$

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

Elliptic curves in class 575.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
575.a1 575e1 \([0, 1, 1, -18, 24]\) \(-5451776/23\) \(-2875\) \([]\) \(56\) \(-0.48171\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 575.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 575.a do not have complex multiplication.

Modular form 575.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{6} - q^{7} + q^{9} - 4 q^{12} - 2 q^{13} + 2 q^{14} - 4 q^{16} + 5 q^{17} - 2 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display