Properties

Label 693b
Number of curves $1$
Conductor $693$
CM no
Rank $1$

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

Elliptic curves in class 693b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
693.c1 693b1 \([0, 0, 1, 18, -7]\) \(884736/539\) \(-392931\) \([]\) \(56\) \(-0.23735\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 693b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 693b do not have complex multiplication.

Modular form 693.2.a.b

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