Properties

Label 684.b
Number of curves $1$
Conductor $684$
CM no
Rank $1$

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

Elliptic curves in class 684.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
684.b1 684a1 \([0, 0, 0, -192, 1028]\) \(-4194304/19\) \(-3545856\) \([]\) \(144\) \(0.10838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 684.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 684.b do not have complex multiplication.

Modular form 684.2.a.b

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