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Properties

Label 478578.d
Number of curves $1$
Conductor $478578$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 478578.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 478578.d do not have complex multiplication.

Modular form 478578.2.a.d

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} - q^{12} + 6 q^{13} + 4 q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 478578.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
478578.d1 478578d1 \([1, 1, 0, -8188, -866144]\) \(-68417929/322704\) \(-286400987873424\) \([]\) \(2448000\) \(1.4587\) \(\Gamma_0(N)\)-optimal