Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 700.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.a1 700g1 \([0, 0, 0, -40, 100]\) \(-221184/7\) \(-224000\) \([]\) \(144\) \(-0.19719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 700.a1 has rank \(1\).

Complex multiplication

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

Modular form 700.2.a.a

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