Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3648.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.b1 3648e1 \([0, -1, 0, -287, -1779]\) \(-40992251392/1539\) \(-98496\) \([]\) \(768\) \(0.044550\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3648.b1 has rank \(1\).

Complex multiplication

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

Modular form 3648.2.a.b

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