Properties

Label 39675.j
Number of curves $1$
Conductor $39675$
CM no
Rank $1$

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

Elliptic curves in class 39675.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39675.j1 39675u1 \([1, 1, 1, -403638, -97797444]\) \(78605490625/985527\) \(91183353486564375\) \([]\) \(456192\) \(2.0638\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39675.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 39675.j do not have complex multiplication.

Modular form 39675.2.a.j

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