Properties

Label 55470j
Number of curves $1$
Conductor $55470$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 55470j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55470.l1 55470j1 \([1, 0, 1, -383, 3026]\) \(-77854483/5760\) \(-457960320\) \([]\) \(24640\) \(0.41078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55470j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 55470j do not have complex multiplication.

Modular form 55470.2.a.j

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