Properties

Label 444675.e
Number of curves $1$
Conductor $444675$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 444675.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444675.e1 444675e1 \([0, -1, 1, -938758, -576618582]\) \(-1376628736/1366875\) \(-90844177545966796875\) \([]\) \(17418240\) \(2.5254\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 444675.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 444675.e do not have complex multiplication.

Modular form 444675.2.a.e

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