Properties

Label 444675hr
Number of curves $1$
Conductor $444675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hr1")
 
E.isogeny_class()
 

Elliptic curves in class 444675hr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444675.hr1 444675hr1 \([0, -1, 1, -857908, 305091093]\) \(313944395776/1240029\) \(275819824849078125\) \([]\) \(14192640\) \(2.2038\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 444675hr1 has rank \(1\).

Complex multiplication

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

Modular form 444675.2.a.hr

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