Properties

Label 3648.q
Number of curves $1$
Conductor $3648$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 3648.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.q1 3648bb1 \([0, -1, 0, 11, -83]\) \(8192/171\) \(-2801664\) \([]\) \(768\) \(-0.082532\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3648.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3648.q do not have complex multiplication.

Modular form 3648.2.a.q

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