Properties

Label 700.b
Number of curves $1$
Conductor $700$
CM no
Rank $1$

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

Elliptic curves in class 700.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.b1 700d1 \([0, 0, 0, 800, 26500]\) \(14155776/84035\) \(-336140000000\) \([]\) \(1440\) \(0.89365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 700.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 700.b do not have complex multiplication.

Modular form 700.2.a.b

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