Properties

Label 47775cm
Number of curves $1$
Conductor $47775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 47775cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47775.n1 47775cm1 \([0, 1, 1, -81258, 13979144]\) \(-32278933504/27421875\) \(-50408690185546875\) \([]\) \(762048\) \(1.9025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47775cm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 47775cm do not have complex multiplication.

Modular form 47775.2.a.cm

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{9} + 5 q^{11} + 2 q^{12} - q^{13} - 4 q^{16} - 7 q^{17} - 2 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display