Properties

Label 2800.a
Number of curves $1$
Conductor $2800$
CM no
Rank $1$

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

Elliptic curves in class 2800.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.a1 2800bb1 \([0, 0, 0, -1000, -12500]\) \(-221184/7\) \(-3500000000\) \([]\) \(2880\) \(0.60753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2800.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2800.a do not have complex multiplication.

Modular form 2800.2.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