Properties

Label 700.j
Number of curves $1$
Conductor $700$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 700.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.j1 700j1 \([0, 0, 0, -1000, 12500]\) \(-221184/7\) \(-3500000000\) \([]\) \(720\) \(0.60753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 700.j1 has rank \(0\).

Complex multiplication

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

Modular form 700.2.a.j

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + q^{7} + 6 q^{9} + 3 q^{11} + q^{13} - 5 q^{17} - 8 q^{19} + O(q^{20})\)  Toggle raw display