Properties

Label 38640.ct
Number of curves $1$
Conductor $38640$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 38640.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.ct1 38640cw1 \([0, 1, 0, -1125, 14175]\) \(-615640662016/978075\) \(-250387200\) \([]\) \(21120\) \(0.50952\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38640.ct1 has rank \(1\).

Complex multiplication

The elliptic curves in class 38640.ct do not have complex multiplication.

Modular form 38640.2.a.ct

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